LIBRARY 


UNIVERSITY  OF  CALIFORNIA. 


UNIVERSITY  OF   CALIFORNIA 

LIBRARY 

OF  THE 

DEPARTMENT   OF   PHYSICS 


NOY1419H 


Received 

Accessions  No. (p  $  fy         Book  No. y  . 


SMITHSONIAN   MISCELLANEOUS   COLLECTIONS 

VOLUME   58,   NUMBER  1 


SMITHSONIAN 

PHYSICAL  TABLES 

FIFTH  REVISED  EDITION 


PREPARED   BY 

F.  E.  FOWLE 

AID.  SMITHSONIAN   ASTROPHYSICAL  OBSERVATORY 


sosr 


(PUBLICATION   1944), 


CITY  OF  WASHINGTON 

PUBLISHED  BY  THE  SMITHSONIAN  INSTITUTION 
1910 


StT 
110 


ADVERTISEMENT. 

In  connection  with  the  system  of  meteorological  observations  established  by 
the  Smithsonian  Institution  about  1850,  a  series  of  meteorological  tables  was 
compiled  by  Dr.  Arnold  Guyot,  at  the  request  of  Secretary  Henry,  and  the  first 
edition  was  published  in  1852.  Though  primarily  designed  for  meteorological 
observers  reporting  to  the  Smithsonian  Institution,  the  tables  were  so  widely  used 
by  physicists  that  it  seemed  desirable  to  recast  the  work  entirely.  It  was  decided 
to  publish  three  sets  of  tables,  each  representative  of  the  latest  knowledge  in  its 
field,  and  independent  of  one  another,  but  forming  a  homogeneous  series.  The 
first  of  the  new  series,  Meteorological  Tables,  was  published  in  1893,  tne  second, 
Geographical  Tables,  in  1894,  and  the  third,  Physical  Tables,  in  1896.  In  1909 
yet  another  volume  was  added,  so  that  the  series  now  comprises  :  Smithsonian 
Meteorological  Tables,  Smithsonian  Geographical  Tables,  Smithsonian  Physical 
Tables,  and  Smithsonian  Mathematical  Tables. 

The  fourteen  years  which  have  elapsed  since  the  publication  of  the  first  edition 
of  the  Physical  Tables,  prepared  by  Professor  Thomas  Gray,  have  brought  such 
changes  in  the  material  upon  which  the  tables  must  be  based  that  it  became 
necessary  to  prepare  this  almost  wholly  new  set  of  tables  for  the  present  edition. 

CHARLES   D.  WALCOTT, 
Secretary -,  Smithsonian  Institution. 

June,  1910. 


222536 


PREFACE. 

The  present  Smithsonian  Physical  Tables  are  the  outcome  of  a  radical  revision 
of  the  set  of  tables  compiled  by  Professor  Thomas  Gray  in  1896.  Recent  data 
and  many  new  tables  have  been  added  for  which  the  references  to  the  sources 
have  been  made  more  complete ;  and  several  mathematical  tables  have  been 
added,  —  some  of  them  especially  computed  for  this  work.  The  inclusion  of  these 
mathematical  tables  seems  warranted  by  the  demand  for  them.  In  order  to  pre- 
serve a  uniform  change  of  argument  and  to  facilitate  comparison,  many  of  the 
numbers  given  in  some  tables  have  been  obtained  by  interpolation  in  the  data 
actually  given  in  the  papers  quoted. 

Our  gratitude  is  expressed  for  many  suggestions  and  for  help  in  the  improve- 
ment of  the  present  edition :  to  the  U.  S.  Bureau  of  Standards  for  the  revision  of 
the  electrical,  magnetic,  and  metrological  tables  and  other  suggestions  \  to  the 
U.  S.  Coast  and  Geodetic  Survey  for  the  revision  of  the  magnetic  and  geodetic 
tables ;  to  the  U.  S.  Geological  Survey  for  various  data ;  to  Mr.  Van  Orstrand  for 
several  of  the  mathematical  tables ;  to  Mr.  Wead  for  the  data  on  the  musical 
scales ;  to  Mr.  Sosman  for  the  new  physical-chemistry  data  ;  to  Messrs.  Abbot, 
Becker,  Lanza,  Rosa,  and  Wood ;  to  the  U.  S.  Bureau  of  Forestry  and  to  others. 
We  are  also  under  obligation  to  the  authors  and  publishers  of  Landolt-Bornstein- 
Meyerhoffer's  Physikalisch-chemische  Tabellen  (1905)  and  B.  O.  Peirce's  Mathe- 
matical Tables  for  the  use  of  certain  tables. 

It  is  hardly  possible  that  any  series  of  tables  involving  so  much  transcribing, 
interpolation,  and  calculation  should  be  entirely  free  from  errors,  and  the  Smith- 
sonian Institution  will  be  grateful,  not  only  for  notice  of  whatever  errors  may  be 
found,  but  also  for  suggestions  as  to  other  changes  which  may  seem  advisable  for 
later  editions. 

F.  E.  FOWLE. 

ASTROPHYSICAL  OBSERVATORY 

OF  THE  SMITHSONIAN  INSTITUTION, 

June,  1910 


TABLE  OF  CONTENTS 


PACK 

Introduction  on  units  of  measurement  and  conversion  factors        .         .  xv 

Units  of  measurement :  general  discussion xv 

Dimension  formulae  for  dynamic  units   .         .         ...         .         .         .  xvii 

"                 "         "    heat  units xxiii 

of  electric  and  magnetic  units  •'  general  discussion        .         .  xxv 

"          formulae  in  electrostatic  system     ......  xxvi 

"  electromagnetic  system        .         .         .         .  xxix 

Practical  units  of  electricity,  legalization  of  .         .         .         .         .         .  xxxiii 

TABLE 

1.  Formulae  for  conversion  factors  :  (a)  Fundamental  units      ...       2 

(b)  Derived  units  ...       2 

I.  Geometric  and  dynamic  units       2 

II.  Heat  units  ....      3 

III.  Magnetic  and  electric  units      3 

2.  Tables  for  converting  U.  S.  weights  and  measures  : 

(1)  Customary  to  metric    ........       5 

(2)  Metric  to  customary     ........       6 

3.  Equivalents  of  metric  and  British  imperial  weights  and  measures : 

(1)  Metric  to  imperial        ........       7 

(2)  Multiples,  metric  to  imperial        ......       8 

(3)  Imperial  to  metric        ........      9 

(4)  Multiples,  imperial  to  metric        .         .         .         .         .         .10 

4.  Volume  of  a  glass  vessel  from  weight  of  its  volume  of  water  or  mercury     1 1 

5.  Elementary  differential  coefficients  and  integrals  .         .         .         .12 

6.  Reciprocals,  squares,  cubes  and  square  roots  of  natural  numbers          .     13 

7.  Logarithms,  1000-2000          .  .         .         .         .         .         .         .22 

8.  Logarithms  ...........     24 

9.  Antilogarithms      .         .         .         .         .         .         .         .         .         .         .     26 

10.  Antilogarithms,  .9000-1.0000         ........     28 

11.  Circular  (trigonometric)  functions,  argument  (° ,'.)       .         .         .         .     30 

12.  "  "  "          argument  (radians)  .         .        .     35 
i2a.  Factorials,  n!,  n  =  i  to  100  .........     38 

13.  Values  of  -       -  (hyperbolic  sines),  for  values  of  x  from  o  to  5  .     39 

14.  Logarithms  of  -  (hyperbolic  sines),  for  values  of  x  from  o  to  5  .     40 

15.  Values  of  -  ^ —  (hyperbolic  cosines),  for  values  of  x  from  o  to  5        .    41 


Vi  CONTENTS. 


20. 


1  6.    Logarithms  of  —  -^  —  (hyperbolic  cosines)  for  values  of  x  from  o  to  5     42 


17.  Values  of  c*  and  e~*  and  their  logarithms  for  x  from  o  to  10 

18.  "      "   log.  ?  for  values  of  x  from  i  o  to  30      .        .        . 

19.  "     "   e*  and  e'3*  and  their  logarithms    .        .        .        . 


"      "4"      "  " 


21.  "      "  e4     and*   *         «  ..... 

22.  "     "    **  and  <r-*  and       "  "          for  fractional  values  of  x 

23.  Probability  of  errors  of  observations  :  probability  integral    .         . 

n  A  <<  «  <<  "  «  «  «< 

24.  .  . 


25.  Values  of  0.6745      ~—^ 

26.  "      "   °'6745  ^-^ri 


29.  Inverse  of  probability  integral.     Diffusion    ...... 

30.  Logarithms  of  the  gamma  function  T(n)  for  values  of  n  between  i  and  2 

31.  Values  for  the  first  seven  zonal  harmonics  from  0  =  o°  to  #  =  90°         . 

32.  "       "    log.  M/q.Tr^/aa1  for  facilitating  the  calculation  of  the  mutual 
inductance  between  two  coaxial  circles      .        .        .        .        .        . 

33.  Value  fory  2(i  —  sm*0sin?<£)±}d<l>    for  different  values  of  0  ;   also   the 

corresponding  logarithms  ......... 

34.  Moments  of  inertia,  radii  of  gyration,  corresponding  weights 

35.  British  standard  wire  gauge  :  diameters,  sections  ..... 

36.  Birmingham  wire  gauge  "  "         ..... 
(For  Brown  and  Sharp  gauge,  see  tables  40  and  41) 

37.  Cross  section  and  weights  of  wires  (copper,  iron,  brass),  British  units  . 

38.  "  "         "          "        "       "  "          "         "         metric  units  . 

39.  "  "         "          "        "  aluminum  wire:  British  and  metric  units  . 

40.  Size,  weight  and  electrical  constants  of  copper  wire,  Brown  and  Sharp 

gauge  :  common  units        ......... 

41.  Same  as  table  40,  but  in  metric  measure        ...... 

42.  Weight  in  grammes  per  square  metre  of  sheet  metal     .... 

43.  "       "  various  common  units  of  sheet  metal     ..... 

44.  Strength  of  materials  :  (a)  metals          ...... 

(b}  stones          .         .        ..... 

(f)  brick    ........ 

(d}  concretes    ....... 

45.  "         "        "  timber  tests       ....... 

Af.          a         «         a  ti         (i 

40.  .        •        •        •        •        ... 

47.    Moduli  of  rigidity         .        .....        .        •        .        . 


CONTENTS.  Vll 

470.  Variation  of  the  moduli  of  rigidity  with  the  temperature       .        .        .     74 

48.  Young's  modulus  ..........     75 

49.  Compressibility  of  the  more  important  solid  elements  .         .         .        -76 

50.  Hardness      ............     76 

51.  Relative  hardness  of  the  elements 76 

52.  Poisson's  ratio      .         .         .         .         .  .         .         .         .         .     76 

53.  Elastic  moduli  of  crystals,  formulae 77 

54.  "  "       "        "         numerical  results 78 

55.  Compressibility  of  O,  air,  N,  H  at  different  pressures  and  temperatures     79 

56.  "  "  ethylene        "         "  "  "  "          .     79 

-„  it  n  «  «  «  it  (6  it  j~ 

58.  "  "  carbon  dioxide  at  "  "  "  "          .     80 

59.  "  gases,  values  of  a    .         .         .         .         .         .         .80 

60.  "  "  air  and  oxygen  between  18°  and  22°C     .         .         .80 

61.  Relation  between  pressure,  temperature  and  volume  of  sulphur  dioxide    81 

62.  "  "  "  "  "         "       "  ammonia  .     81 

63.  Compressibility  of  liquids 82 

64.  "  "       " 83 

65.  Specific  gravities  corresponding  to  the  Beaume'  scale    .         .        .         .84 

66.  Densities  of  the  solid  and  liquid  elements 85 

67.  "  various  woods   . 87 

68.  "         "        "       solids 88 

69.  "          "        "       alloys 89 

70.  "          "        "       liquids 90 

71.  "          "        "       gases 91 

72.  "         "        "       aqueous  solutions  of  salts,  bases  and  acids    .        .    92 

73.  Density  of  water  between  o°  and  36°  C        ......     94 

74.  Volume  of  water  at  temperatures  between  o°  and  36°  C  in  terms  of  its 

volume  at  the  temperature  of  maximum  density       .         .        .         -95 

75.  Density  and  volume  of  water  at  different  temperatures  from  -10  to  25o°C     96 

76.  "         "         "        "  mercury  at  "  "  "     -10  "  36o°C     97 

77.  Specific  gravity  of  aqueous  ethyl  alcohol      ......     98 

78.  Density  of  aqueous  methyl  alcohol        .......     99 

79.  Variation  of  the  density  of  alcohol  with  the  temperature       .         .         .100 

80.  Velocity  of  sound  in  solids  .........  101 

8 1.  "         "      "       "  liquids  and  gases 102 

82.  Musical  scales 103 

83.  "          " 103 

84.  Force  of  gravity  at  sea  level  and  different  latitudes      .         .         .         .104 

85.  Results  of  some  of  the  more  recent  gravity  determinations  .         .        .  105 

86.  Value  of  gravity  at  some  of  the  U.  S.  C.  and  G.  Survey  stations  .        .106 

87.  Length  of  seconds  pendulum  for  sea  level  and  different  latitudes          .  107 

88.  Determinations  of  the  length  of  the  seconds  pendulum         .        .         .  107 

89.  Miscellaneous  data  as  to  the  earth  and  planets     .         .         .        .        .108 

90.  Terrestrial  magnetism  :  secular  change  of  declination  .         .        .no 

91.  "  "  dip  or  inclination 112 

92.  "  secular  change  of  dip 112 

93.  "  "  horizontal  intensity 113 


Vlll  CONTENTS. 

94.  Terrestrial  magnetism :  secular  change  of  horizontal  intensity      .         -113 

95.  "  "  total  intensity 114 

96.  "  "  secular  change  of  total  intensity      .        ,         .114 

97.  "  "  agonic  line      .         .         .  *       ;,         .  115 

98.  Pressure  of  mercury  and  water  columns        .         .        .        .        •        .116 

99.  Reduction  of  barometer  to  standard  temperature .         .         .        .        .  117 

100.  "          "         "          "        "         gravity,  inch  and  metric  scales     .  118 

101.  "          "         "          "  latitude  45°  :  inch  scale      .        .        v        .119 

102.  "          "          "          "        "        "     metric  scale    .        .        ,.        .  120 

103.  Correction  of  barometer  for  capillarity  :  inch  and  metric  scale     .         .121 

104.  Aerodynamics:  data  for  wind  pressures        .         .         .         .        •        .122 

105.  "  "       "    the  soaring  of  planes 123 

1 06.  Coefficients  of  friction  .         .         .         .         .         .         .         .         .  .124 

107.  Viscosity  of  water  at  different  temperatures          .         .         .         .  .  125 

108.  Coefficients  of  viscosity  for  solutions  of  alcohol  in  water       .         .  .126 

109.  Specific  viscosity  of  mineral  oils   .         .         .         .        •        »        .  .126 

no.         "  "          "  various  oils >        «  .  126 

in.         "  "          "       "       liquids .127 

112.  "  "         "        "  "       temperature  variation     .      --Y        .  128 

113.  "          "  solutions:  variation  with  density  and  temperature.  129 

114.  "  "          "         "          atomic  concentrations    ....  133 

115.  "  "         "  gases  and  vapors   .        .        .        .        .        .        .  134 

116.  "  u         "      "        "         "       temperature  variation          .         .  135 

117.  Diffusion  of  an  aqueous  solution  into  pure  water 136 

118.  "         "  vapors      7~ 137 

119.  "  gases  and  vapors       ........  138 

1190.  "  metals  into  metals     ........  138 

120.  Solubility  of  inorganic  salts  in  water:  temperature  variation         .         .  139 

121.  "          "  a  few  organic  salts  in  water :  temperature  variation  .         .  140 

122.  "         "  gases  in  water .        .  140 

123.  Absorption  of  gases  by  liquids      .         .         .         .         .         .         .         .141 

124.  Capillarity  and  surface  tension  :  water  and  alcohol  in  air  .        .142 

125.  "  "         "  "         miscellaneous  liquids  in  air          .         .  142 

126.  "  aqueous  solutions  of  salts    .         .         .142 

127.  Capillarity  and  surface  tension :  liquids  in  contact  with  air,  water  or 

mercury  ........... 

128.  Capillarity  and  surface  tension  :  liquids  at  solidifying  point  . 

129.  "  "         "  "        thickness  of  soap  films 

130.  Vapor  pressures 

131.  "  "         of  ethyl  alcohol  .         .         .        . 

132.  "  "          "  methyl    " 

133.  and  temperatures :  (a)  carbon  disulphide  . 

(b)  chlorobenzine 

(c)  bromobenzine 

(d)  aniline   .... 
(<?)  methyl  salicylate    . 

(f)  bromonaphthaline . 

(g)  mercury 


CONTENTS.  IX 

134.  Vapor  pressures  of  solutions  of  salts  in  water 149 

135.  Pressure  of  aqueous  vapor  at  low  temperatures    .        .         .        .        .  151 

136.  "         "         "  "      o°  to  100°  C  (Broch) 152 

137.  "         "         "  "      100°  to  230°  C  (Regnault)  .         .         .         .153 

138.  Weight  in  grains  of  aqueous  vapor  in  a  cubic  foot  of  saturated  air      .  154 
139-          "       "  grammes  of     "  "     "  "     "      metre  of       "          "       .  154 

140.  Hygrometry,  vapor  pressure  in  the  atmosphere 155 

141.  "  dew-points        .........  156 

142.  Relative  humidity         ..........  158 

143.  Values  of  0.378*?  in  the  atmospheric  pressure  equation  h=.B  —  0.3781?.  159 

144.  Table  for  facilitating  the  calculation  of  ^760       .....  160 

145.  Logarithms  of  ^760  for  values  of  h  between  80  and  800      .         .         .  160 

146.  Values  of  1-1-0.00367  t\ 

(a)  for  values  of  /between  o°  and  10°  C,  by  tenths  .         .         .  162 

(b)  "        "      "  "       "  —90°    "    +1990°  C,  by  tens       .        .  163 
(f)  logarithms  for  t     "  — 49°    "    +399°  c»  bv  units         •        •  l64 
(d)          «  «    "     "    400°    "    1990°  C,  by  tens  .         .         .166 

147.  Determination  of  heights  by  the  barometer  ......  167 

148.  Barometric  pressures  corresponding  to  different  temperatures  of  the 

boiling-point  of  water : 

(a)  Common  measure         .         .         .         .         .         .         .         .168 

(<£)  Metric  measure    .........  169 

149.  Standard  wave-lengths :  Fabry-Buisson's  iron  arc  lines          .         .         .  170 

150.  "  "          "          red  cadmium  line 170 

151.  Stronger  lines  of  some  of  the  elements          .         .  .         .         .170 

152.  Rowland's  standard  solar  wave-lengths  (also  corrections)     .         .         .  171 

153.  Kayser's  standard  iron  arc  lines  (also  corrections)         ....  174 

154.  Wave-lengths  of  the  Fraunhofer  lines    .         .         .         .         .         .         .176 

155.  Photometric  standards  ..........  177 

156.  Sensitiveness  of  the  eye  to  radiation  of  different  wave-lengths:  low 

(threshold)  intensities         .         .         .         .         .         .         .         .         .178 

157.  Sensitiveness  of  the  eye  :  greater  intensities  .         .....  178 

158.  Sensibility  of  the  eye  to  small  differences  of  intensity  (Fechner)  .         .178 

159.  Solar  energy  and  its  absorption  by  the  earth's  atmosphere    .         .        .  179 

1 60.  The  solar  "  constant "  of  radiation  and  temperature  of  sun  .         .         .  179 

161.  Distribution  of  intensity  of  radiation  over  solar  disk     .         .         .        .  179 

162.  Relative  intensities  of  sunlight  and  sky-light         .         .         .  .  179 

163.  Indices  of  refraction  of  Jena  glasses 180 

164.  MM  «  «     «          « !8o 

165.  "       "  "  "     "          "       temperature  coefficients        .        .  180 

166.  "       "  "  "  various  alums 181 

167.  "       "  "  "  metals  and  metallic  oxides : 

(a)  Kundt's  experiments 182 

(b)  Du  Bois  and  Rubens'  experiments       .         .         .         .         .  182 
(<r)  Drude's  experiments 182 

168.  Indices  of  refraction  for  rock  salt 183 

169.  "       "          "          "      "       "     temperature  coefficients  .        .        .183 

170.  "       "          "  "    sylvine 183 


*  X  CONTENTS. 

171.    Indices  of  refraction  for  fluorite 184 

,  172.  "       "          "          "         "        temperature  coefficients     .        .         .  184 

v  173.         "        "          "  "    Iceland  spar 'V        .  184 

:  174.  "       "          "           "    nitroso-dimethyl-aniline  .         .                 .         .  184 

175.  "       «          "  "    quartz 185 

176.  "        "          "  "    various  monorefringents 186 

177.  "       "          "  "         "       uniaxial  crystals 187 

178.  "       "          "  "         "       biaxial  crystals 187 

179.  "       "  "           "    solutions  of  salts  and  acids  : 

(a)  solutions  in  water          .         .         .         .188 

(b)  «         "   alcohol       .         .         .         .188 

(c)  "         "   potassium  permanganate    .  188 

180.  "         "          "  "    various  liquids 189 

181.  "         "          "  "    gases  and  vapors 190 

182.  Reflection  of  light,  perpendicular  incidence  :  various  values  of  n  .         .  191 

183.  "          "     "      incidence  varying :  n  near  unity      ....  191 

184.  "         "     "  "              "          «=i.55    •         •        •        •         .191 

185.  Reflection  from  metals 192 

1 86.  Transmission  of  Jena  glasses        .        .        .        .  .        .         .  193 

187.  "  "      " 193 

188.  "  "      "     ultra-violet  glasses 193 

189.  "  "  alum,  rock  salt,  sylvine,  fluorite,  Iceland  spar,  quartz     194 

190.  Color  screens  (Landolt) 195 

191.  "          "       (Wood) 195 

192.  "  "        (Jena  glasses)         ........  196 

193.  Rotation  of  the  plane  of  polarized  light  by  solutions     ....  197 

194.  "         "    "       "       "          "  "      "     sodium  chlorate  and  quartz  197 

195.  Colors  of  thin  films,  Newton's  rings 198 

196.  Thermal  conductivity  of  metals  and  alloys 199 

197.  "  "            "  various  substances ......  200 

198.  "  "            "  water  and  salt  solutions .         •         .         .         .200 

199.  "  "  "  organic  liquids 200 

200.  "  "  "  gases 200 

201.  Heat  of  combustion       .         .         .         .         .         .         .         .         .         .  201 

202.  Heat  values  and  analyses  of  various  fuels :  (a)  coals    ....  202 

(fr)  peats    .         .         .         .202 
(c)  liquid  fuels  .        .         .202 

203.  Chemical  and  physical  properties  of  explosives     .        .        .        .        .  203 

204.  Heat  of  combination     ..........  204 

205.  Latent  heat  of  vaporization 206 

206.  "         "      "  fusion 208 

207.  Melting-points  of  the  chemical  elements 209 

208.  Boiling-points    "     "          "  "  210 

209.  Melting-points  of  various  inorganic  compounds    .         •         •         .         .211 

210.  Boiling-points    "        "  "  "  213 

211.  Melting  points  of  various  mixtures  of  metals        .        •        •        .       .-214 

212.  "  "         "  "  "  "         " 214 

213.  Low-melting-point  alloys       .. .214 


CONTENTS.  XI 

214.  Densities,  melting-points,  boiling-points  of  organic  compounds: 

(a)    Paraffin  series .215 

(£)    Olefine  series 215 

(f)    Acetylene  series 216 

(d)  Monatomic  alcohols 216 

(e)  Alcoholic  ethers 216 

(/)  Ethyl  ethers          .         .         .         .         .         .         .         .        .216 

215.  Lowering  of  freezing-points  by  salts  in  solution 217 

216.  Raising  of  boiling-points  by  salts  in  solution 219 

217.  Freezing  mixtures          ..........  220 

218.  Critical  temperatures,  pressure,  volumes  and  densities  of  gases    .         .221 

219.  Coefficients  of  linear  expansion  of  the  chemical  elements     .         .         .222 

220.  "  "       "  "          "  miscellaneous  substances         .         .  223 

221.  "  "  cubical       "  "   crystalline  and  other  solids     .         .  224 

222.  "  "         "  "          "   liquids 225 

223.  "  "    thermal  expansion  of  gases 226 

224.  Mechanical  equivalent  of  heat:  various  data        .....  227 

225.  "  "          "     "      adopted  values  (Ames)        .        .        .  227 

226.  "  "         "     "     conversion  values         .        .        .        .227 

227.  Specific  heats  of  the  chemical  elements 228 

228.  "  "  "  water  and  mercury 229 

229.  "  "  "  various  solids 230 

230.  "  "  "        "       liquids 230 

231.  "  "  "        "       minerals  and  rocks 231 

232.  "  "  "        "       gases  and  vapors    ......  232 

233.  Gas  and  mercury  thermometers :  formulae 233 

234.  Comparison  of  hydrogen  and  i6m  thermometers :  o°  to  100°  C.       .         .  233 

235.  "  "         "  "   59IU  "  o°toioo°C.      .        .233 

236.  "  "         "  "    16'" and  59™ thermometers:  -5°  to  -35°  C.  233 

237.  Comparison  of  air  and  i6m  glass  thermometers  :  o°  to  300°  C.     .         .  234 

238.  "  "   "     "     59m    "  "  100°  to  200°  C.          .  234 

239.  "  "  hydrogen  and  various  mercury  thermometers         .         .  235 

240.  "  "  air  and  high  temperature  (59m)  mercury  thermometer  .  235 

241.  "            "  H.,   toluol,  alcohol,  petrol  ether,  pentane  thermome- 
ters        235 

242.  Stem  correction  for  thermometers 236 

243-       "  "  " 237 

244.  "  "  237 

245.  Radiation  formulae  and  constants  for  perfect  radiator  .        .        .        .238 

246.  "         in  calories  for  perfect  radiators  at  various  temperatures        .  238 

247.  "         distribution  in  spectrum  at  various  temperatures  .         .         .  238 

248.  Cooling  by  radiation  and  convection  ;  ordinary  pressures     .         .         .  239 

249.  "        "         "  "            "           different  pressures      .        .        .  239 

250.  "         "         "  "             "           very  small  pressures  .         .        .  240 

251.  Cooling  by  radiation  and  convection  :  temperature  and  pressure  effects  240 

252.  Properties  and  constants  of  saturated  steam :  metric  measure       .         •  241 

253.  "  "          "          "         "             "        common  measure   .        .  242 

254.  Ratio  of  the  electrostatic  to  the  electromagnetic  unit  of  electricity       .  247 


Xl  CONTENTS. 

255.  Dielectric  strength ;  steady  potential  for  spark  in  air    .        .        .        .248 

256.  "  "          alternating  potential  for  spark  in  air     .         .        .  248 

257.  "         potentials  for  longer  sparks  in  air          ...  249 

258.  "  "         effect  of  (air)  pressure  ......  249 

259.  "  "          of  various  materials       .         .        ,         .         .         .  250 

260.  "  "          u  kerosene    .  ......  250 

261.  Electromotive  force  of  standard  cells :  absolute  current  measures         .  251 

262.  Data  for  voltaic  cells  :  (a)  double  fluid  cells 252 

(b)  single  fluid  cells          .....  253 

(c)  standard  cells     ......  253 

(d)  secondary  (storage)  cells    ....  253 

263.  Contact  differences  of  potential,  solids  with  liquids  and  liquids  with 

liquids  in  air 254 

264.  Contact  differences  of  potential,  solids  with  solids  in  air  .         .  256 

265.  Potential  difference  between  metals  in  various  salt  solutions         .         .  257 

266.  Thermoelectric  powers          .........  258 

267.  "  "       with  platinum 259 

268.  Peltier  effect 260 

269.  Various  determinations  of  the  ohm 261 

270.  Specific  resistance  of  metallic  wires       .......  262 

271.  "  "          "  metals 263 

272.  Resistance  of  metals  and  alloys  at  low  temperatures     .         .         .         .264 

273.  Conductivity  of  three-metal  and  miscellaneous  alloys    ....  266 

274.  Conducting  power  of  alloys 267 

275.  Electric  resistance  with  alternating  currents  (straight  wires)         .         .  269 

276.  International  atomic  weights  and  electrochemical  equivalents       .         .  270 

277.  Conductivity  of  a  few  dilute  solutions 272 

278.  Electrochemical  equivalents  and  densities  of  nearly  normal  solutions  .  272 

279.  Specific  molecular  conductivity  of  solutions  .         .         .         .         .         .  273 

280.  "  "  "  "         "         limiting  values  .         .         .  274 

281.  "  "  "  "         "         temperature  coefficients     .  274 

282.  Equivalent  conductivity  of  salts,  acids,  bases  in  solution       .        .         .  275 

283.  "  "  "  some  additional  salts  in  solution          .         -277 

284.  "        conductance  of  the  separate  ions 278 

285.  Hydrolysis  of  ammonium  acetate  :  ionization  of  water  .         .         .         .278 

286.  Dielectric  constants  (specific  inductive  capacity)  of  gases     .         .         -279 

287.  "              "                 "            "                "         "      "       temperature 
coefficient 279 

288.  Dielectric  constants  (specific  inductive  capacity)  of  gases  :  pressure  co- 

efficient    ............  279 

289.  Dielectric  constants  of  liquids ^ .  280 

290.  "  "          "       "     temperature  coefficient     ....  282 

291.  "  "  liquefied  gases 282 

292.  "  "  standard  solutions  for  calibrations      .        .        .  283 

293.  Dielectric  constants  of  solids 283 

294.  "  "          "  crystals 284 

295.  Temperature  variation  of  electrical  resistance  of  glass,  porcelain  .         .  285 

296.  Permeability  of  iron  rings  and  wire,  various  inductions          .        .        .  286 


CONTENTS.  xiii 

297.  Permeability  of  transformer  iron  : 

(a)  specimen  of  Westinghouse  No.  8  transformer        .        .         .  286 
(*)          "  "  "    6  287 

(V)  "  "  "    4          "         .         .  287 

(d)         "          "   Thomson-Houston  1 5oo-watt  transformer  .         .  287 

298.  Magnetic  properties  of  iron  and  steel     .......  288 

299.  "  "  "  cast  iron  in  intense  fields 288 

300.  "       corrections  for  ring  specimens         ......  288 

301.  Demagnetizing  factors  for  rods      ........  289 

302.  "  "       Shuddemagen's  values        .....  289 

303.  Composition  and  magnetic  properties  of  iron  and  steel          .        .        .  290 

304.  Permeability  of  some  of  the  specimens  in  Table  303      ....  292 

305.  Magnetic  properties  of  soft  iron  at  o°  and  100°  C 292 

306.  "  "          "  steel  at  o°  and  100°  C 292 

307.  "  "          "  cobalt  at  100°  C 293 

308.  "  "          "  nickel  "      "     " 293 

309.  "  "          "  magnetite           .......  293 

310.  "  "          "  Lowmoor  wrought  iron      .....  293 

311.  "  "          "  Vicker's  tool  steel 293 

312.  "  "          "  Hadfield's  manganese  steel        ....  293 

313.  Saturation  values  for  different  steels 293 

314.  Magnetic  properties  of  iron  in  very  weak  fields 294 

315.  Dissipation  of  energy  in  cyclic  magnetization  of  magnetic  substances    .  294 

316.  "  "        "        "       "              m  "             "  cable  transformers        .  294 

317.  "  "        "       "       "                "             "  various  substances         .295 

318.  "  "       "       "      "                "            "  transformer  steels         .296 

319.  Magneto-optic  rotation,  formulae :  Verdet's  constant      ....  297 

320.  "  "  "         in  solids 298 

321.  "  "  "         "  liquids 299 

322.  "  "           "         "  solutions  of  salts  and  acids  in  water     .         .  301 

323.  "  "           "         "         "          "      "     in  alcohol  .         .         .         .303 

324.  "  "          "         "        "         "      "     "  hydrochloric  acid  .        .  303 

325.  "  «          "        "    gases  ....                 ...  304 

326.  Verdet's  and  Kundt's  constants 304 

327.  Magnetic  susceptibility  of  liquids  and  gases  ......  305 

328.  Values  of  Kerr's  constant      .........  305 

329.  Variation  of  the  resistance  of  bismuth  in  magnetic  field         .         .         .  306 

330.  «         "     "  "          "   nickel      "          "           "  .                             306 

331.  "        "     "  "         "  various  metals  in  a  magnetic  field    .        .306 

332.  Transverse  galvanomagnetic  and  thermomagnetic  effects       .         .        .  307 

333.  Variation  of  the  Hall  constant  with  the  temperature      ....  307 

334.  Appendix :  Mean  specific  heat  of  iron  at  high  temperatures  .        .        .  308 

335.  Total  heat  of  iron  to  high  temperatures       ....  308 
—             "  Definitions  of  units 309 


Index 313 


INTRODUCTION. 


UNITS   OF  MEASUREMENT  AND   CONVERSION  FORMULA. 

Units.  —  The  quantitative  measure  of  anything  is  a  number  which  expresses  the 
ratio  of  the  magnitude  of  the  thing  to  the  magnitude  of  some  other  thing  of  the 
same  kind.  In  order  that  the  number  expressing  the  measure  may  be  intelligi- 
ble, the  magnitude  of  the  thing  used  for  comparison  must  be  known.  This  leads 
to  the  conventional  choice  of  certain  magnitudes  as  units  of  measurement,  and 
any  other  magnitude  is  then  simply  expressed  by  a  number  which  tells  how  many 
magnitudes  equal  to  the  unit  of  the  same  kind  of  magnitude  it  contains.  For 
example,  the  distance  between  two  places  may  be  stated  as  a  certain  number  of 
miles  or  of  yards  or  of  feet.  In  the  first  case,  the  mile  is  assumed  as  a  known 
distance ;  in  the  second,  the  yard,  and  in  the  third,  the  foot.  What  is  sought  for 
in  the  statement  is  to  convey  an  idea  of  the  distance  by  describing  it  in  terms  of 
distances  which  are  either  familiar  or  easily  referred  to  for  comparison.  Similarly 
quantities  of  matter  are  referred  to  as  so  many  tons  or  pounds  or  grains  and  so 
forth,  and  intervals  of  time  as  a  number  of  hours  or  minutes  or  seconds.  Gen- 
erally in  ordinary  affairs  such  statements  appeal  to  experience  j  but,  whether  this 
be  so  or  not,  the  statement  must  involve  some  magnitude  as  a  fundamental  quan- 
tity, and  this  must  be  of  such  a  character  that,  if  it  is  not  known,  it  can  be  readily 
referred  to.  We  become  familiar  with  the  length  of  a  mile  by  walking  over  dis- 
tances expressed  in  miles,  with  the  length  of  a  yard  or  a  foot  by  examining  a  yard 
or  a  foot  measure  and  comparing  it  with  something  easily  referred  to,  —  say  our 
own  height,  the  length  of  our  foot  or  step,  —  and  similarly  for  quantities  of  other 
kinds.  This  leads  us  to  be  able  to  form  a  mental  picture  of  such  magnitudes 
when  the  numbers  expressing  them  are  stated,  and  hence  to  follow  intelligently 
descriptions  of  the  results  of  scientific  work.  The  possession  of  copies  of  the 
units  enables  us  by  proper  comparisons  to  find  the  magnitude-numbers  express- 
ing physical  quantities  for  ourselves.  The  numbers  descriptive  of  any  quan- 
tity must  depend  on  the  intrinsic  magnitude  of  the  unit  in  terms  of  which  it  is 
described.  Thus  a  mile  is  1760  yards,  or  5280  feet,  and  hence  when  a  mile  is 
taken  as  the  unit  the  magnitude-number  for  the  distance  is  i,  when  a  yard  is  taken 
as  the  unit  the  magnitude-number  is  1760,  and  when  afoot  is  taken  it  is  5280. 
Thus,  to  obtain  the  magnitude-number  for  a  quantity  in  terms  of  a  new  unit  when 
it  is  already  known  in  terms  of  another  we  have  to  multiply  the  old  magnitude- 
number  by  the  ratio  of  the  intrinsic  values  of  the  old  and  new  units ;  that  is,  by 
the  number  of  the  new  units  required  to  make  one  of  the  old. 


XVi  INTRODUCTION. 

Fundamental  Units  of  Length  and  Mass.  —  It  is  desirable  that  as  few  dif- 
ferent kinds  of  unit  quantities  as  possible  should  be  introduced  into  our  measure- 
ments, and  since  it  has  been  found  possible  and  convenient  to  express  a  large 
number  of  physical  quantities  in  terms  of  length  or  mass  or  time  units  and  com- 
binations of  these  they  have  been  very  generally  adopted  as  fundamental  units. 
Two  systems  of  such  units  are  used  in  this  country  for  scientific  measurements, 
namely,  the  British,  and  the  French  or  metric,  systems.  Tables  of  conversion 
factors  are  given  in  the  book  for  facilitating  comparisons  between  quantities  ex- 
pressed in  terms  of  one  system  with  similar  quantities  expressed  in  the  other.  In 
the  customary  system  the  standard  unit  of  length  is  the  yard  and  is  now  defined 
as  3600/3937  metre.  The  unit  of  mass  is  the  avoirdupois  pound  and  is  denned 
as  1/2.20462  kilogramme. 

The  British  yard  is  defined  as  the  "  straight  line  or  distance  (at  62°  F.)  between 
the  transverse  lines  in  the  two  gold  plugs  in  the  bronze  bar  deposited  in  the  office 
of  the  exchequer."  The  British  standard  of  mass  is  the  pound  avoirdupois  and 
is  the  mass  of  a  piece  of  platinum  marked  "P.  S.  1844,  i  lb.,"  preserved  in  the 
exchequer  office. 

In  the  metric  system  the  standard  of  length  is  defined  as  the  distance  between 
the  ends  of  a  certain  platinum  bar  (the  metre  des  Archives)  when  the  whole  bar  is 
at  the  temperature  o°  Centigrade.  The  bar  was  made  by  Borda,  and  is  preserved 
in  the  national  archives  of  France.  A  line-standard  metre  has  been  constructed 
by  the  International  Bureau  of  Weights  and  Measures,  and  is  known  as  the  Inter- 
national Prototype  Metre.  A  number  of  standard-metre  bars  which  have  been 
carefully  compared  with  the  International  Prototype  have  lately  been  made  by  the 
International  Bureau  of  Weights  and  Measures  and  furnished  to  the  various  gov- 
ernments who  have  contributed  to  the  support  of  that  bureau.  These  copies  are 
called  National  Prototypes. 

Borda,  Delambre,  Laplace,  and  others,  acting  as  a  committee  of  the  French 
Academy,  recommended  that  the  standard  unit  of  length  should  be  the  ten  mil- 
lionth part  of  the  length,  from  the  equator  to  the  pole,  of  the  meridian  passing 
through  Paris.  In  1795  the  French  Republic  passed  a  decree  making  this  the 
legal  standard  of  length,  and  an  arc  of  the  meridian  extending  from  Dunkirk  to 
Barcelona  was  measured  by  Delambre  and  Mechain  for  the  purpose  of  realizing 
the  standard.  From  the  results  of  that  measurement  the  metre  bar  was  made 
by  Borda.  The  metre  is  not  now  defined  as  stated  above,  but  as  the  length  of 
Borda's  rod,  and  hence  subsequent  measurements  of  the  length  of  the  meridian 
have  not  affected  the  length  of  the  metre. 

The  French,  or  metric,  standard  of  mass,  the  kilogramme,  is  the  mass  of  a 
piece  of  platinum  also  made  by  Borda  in  accordance  with  the  same  decree' of  the 
Republic.  It  was  connected  with  the  standard  of  length  by  being  made  as  nearly 
as  possible  of  the  same  mass  as  that  of  a  cubic  decimetre  of  distilled  water  at 
the  temperature  of  4°  C.,  or  nearly  the  temperature  of  maximum  density. 

As  in  the  case  of  the  metre,  the  International  Bureau  of  Weights  and  Measures 
has  made  copies  of  the  kilogramme.  One  of  these  is  taken  as  a  standard,  and 


INTRODUCTION.  XV11 

is  called  the  International  Prototype  Kilogramme.  The  others  were  distrib- 
uted in  the  same  manner  as  the  metre  standards,  and  are  called  National  Proto- 
types. 

Comparisons  of  the  French  and  customary  standards  are  given  in  tabular  form 
in  Table  2  ;  and  similarly  Table  3,  differing  slightly,  compares  the  British  and 
French  systems.  In  the  metric  system  the  decimal  subdivision  is  used,  and  thus 
we  have  the  decimetre,  the  centimetre,  and  the  millimetre  as  subdivisions,  and 
the  dekametre,  hektometre,  and  kilometre  as  multiples.  The  centimetre  is  most 
commonly  used  in  scientific  work. 

Time.  —  The  unit  of  time  in  both  the  systems  here  referred  to  is  the  mean 
solar  second,  or  the  86,4ooth  part  of  the  mean  solar  day.  The  unit  of  time  is 
thus  founded  on  the  average  time  required  for  the  earth  to  make  one  revolution 
on  its  axis  relatively  to  the  sun  as  a  fixed  point  of  reference. 

Derived  Units.  — Units  of  quantities  depending  on  powers  greater  than  unity 
of  the  fundamental  length,  mass,  and  time  units,  or  on  combinations  of  different 
powers  of  these  units,  are  called  "  derived  units."  Thus,  the  unit  of  area  and  of 
volume  are  respectively  the  area  of  a  square  whose  side  is  the  unit  of  length  and 
the  volume  of  a  cube  whose  edge  is  the  unit  of  length.  Suppose  that  the  area  of 
a  surface  is  expressed  in  terms  of  the  foot  as  fundamental  unit,  and  we  wish  to 
find  the  area-number  when  the  yard  is  taken  as  fundamental  unit.  The  yard  is 
3  times  as  long  as  the  foot,  and  therefore  the  area  of  a  square  whose  side  is  a 
yard  is  3  X  3  times  as  great  as  that  whose  side  is  a  foot.  Thus,  the  surface  will 
only  make  one  ninth  as  many  units  of  area  when  the  yard  is  the  unit  of  length  as 
it  will  make  when  the  foot  is  that  unit.  To  transform,  then,  from  the  foot  as  old 
unit  to  the  yard  as  new  unit,  we  have  to  multiply  the  old  area-number  by  1/9,  or  by 
the  ratio  of  the  magnitude  of  the  old  to  that  of  the  new  unit  of  area.  This  is  the 
same  rule  as  that  given  above,  but  it  is  usually  more  convenient  to  express  the 
transformations  in  terms  of  the  fundamental  units  directly.  In  the  above  case, 
since  on  the  method  of  measurement  here  adopted  an  area-number  is  the  product 
of  a  length-number  by  a  length-number  the  ratio  of  two  units  is  the  square  of  the 
ratio  of  the  intrinsic  values  of  the  two  units  of  length.  Hence,  if  /  be  the  ratio 
of  the  magnitude  of  the  old  to  that  of  the  new  unit  of  length,  the  ratio  of  the  cor- 
responding units  of  area  is  /2.  Similarly  the  ratio  of  two  units  of  volume  will  be 
/*,  and  so  on  for  other  quantities. 

Dimensional  Formulae.  —  It  is  convenient  to  adopt  symbols  for  the  ratios 
of  length  units,  mass  units,  and  time  units,  and  adhere  to  their  use  throughout ; 
and  in  what  follows,  the  small  letters,  /,  m,  t,  will  be  used  for  these  ratios.  These 
letters  will  always  represent  simple  numbers,  but  the  magnitude  of  the  number 
will  depend  on  the  relative  magnitudes  of  the  units  the  ratios  of  which  they  repre- 
sent. When  the  values  of  the  numbers  represented  by  /,  m,  t  are  known,  and  the 
powers  of  /,  m,  and  /  involved  in  any  particular  unit  are  also  known,  the  factor  for 
transformation  is  at  once  obtained.  Thus,  in  the  above  example,  the  value  of  / 
was  1/3  and  the  power  of  /involved  in  the  expression  for  area  is  /*;  hence,  the 
factor  for  transforming  from  square  feet  to  square  yards  is  1/9.  These  factors 


XV111  INTRODUCTION. 

have  been  called  by  Prof.  James  Thomson  "change  ratios,"  which  seems  an 
appropriate  term.  The  term  "  conversion  factor  "  is  perhaps  more  generally 
known,  and  has  been  used  throughout  this  book. 

Conversion  Factor.  —  In  order  to  determine  the  symbolic  expression  for  the 
conversion  factor  for  any  physical  quantity,  it  is  sufficient  to  determine  the  degree 
to  which  the  quantities  length,  mass,  and  time  are  involved  in  the  quantity.  Thus, 
a  velocity  is  expressed  by  the  ratio  of  the  number  representing  a  length  to  that 
representing  an  interval  of  time,  or  L/T,  an  acceleration  by  a  velocity-number 
divided  by  an  interval  of  time-number,  or  L/T2,  and  so  on,  and  the  correspond- 
ing ratios  of  units  must  therefore  enter  to  precisely  the  same  degree.  The  fac- 
tors would  thus  be  for  the  above  cases,  ///  and  ///2.  Equations  of  the  form  above 
given  for  velocity  and  acceleration  which  show  the  dimensions  of  the  quantity  in 
terms  of  the  fundamental  units  are  called  "  dimensional  equations."  Thus 


is  the  dimensional  equation  for  energy,  and  MLaT~2  is  the  dimensional  formula 
for  energy. 

In  general,  if  we  have  an  equation  for  a  physical  quantity 

Q=CLaM6Tc, 

where  C  is  a  constant  and  LMT  represents  length,  mass,  and  time  in  terms  of  one 
set  of  units,  and  we  wish  to  transform  to  another  set  of  units  in  terms  of  which 

T       TiyT     T* 

the  length,  mass,  and  time  are  LyMyTy,  we  have  to  find  the  value  of  _  ',—  J     ',  which 

J_/    JYl    1 

in  accordance  with  the  convention  adopted  above  will  be  /  m  t,  or  the  ratios  of 
the  magnitudes  of  the  old  to  those  of  the  new  units. 

Thus  Ly  =  L/,  My  =  Mm,  Ty  =  T/,  and  if  Qy  be  the  new  quantity-number 

Q,  =  CL/-M,T/' 

=  CLataMbmbTctc  = 


or  the  conversion  factor  is  PnPf,  a  quantity  of  precisely  the  same  form  as  the 
dimension  formula  LaM6Tc. 

We  now  proceed  to  form  the  dimensional  and  conversion  factor  formulae  for 
the  more  commonly  occurring  derived  units. 

1.  Area.  —  The  unit  of  area  is  the  square  the  side  of  which  is  measured  by 
the  unit  of  length.     The  area  of  a  surface  is  therefore  expressed  as 

S  =  CL2, 

where  C  is  a  constant  depending  on  the  shape  of  the  boundary  of  the  surface 
and  L  a  linear  dimension.  For  example,  if  the  surface  be  square  and  L  be  the 
length  of  a  side  C  is  unity.  If  the  boundary  be  a  circle  and  L  be  a  diameter 
C  =  ir/4,  and  so  on.  The  dimensional  formula  is  thus  L2,  and  the  conversion 
factor  /*. 

2.  Volume.  —  The  unit  of  volume  is  the  volume  of  a  cube  the  edge  of  which 
is  measured  by  the  unit  of  length.    The  volume  of  a  body  is  therefore  expressed  as 


INTRODUCTION.  XIX 

V  =  CL8, 

where  as  before  C  is  a  constant  depending  on  the  shape  of  the  boundary.     The 
dimensional  formula  is  L8  and  the  conversion  factor  /8. 

3.  Density.  —  The  density  of  a  substance  is  the  quantity  of  matter  in  the  unit 
of  volume.     The  dimension  formula  is  therefore  M/V  or  ML~8,  and  conversion 
factor  ml~*. 

Example.  —  The  density  of  a  body  is  150  in  pounds  per  cubic  foot:  required 
the  density  in  grains  per  cubic  inch. 

Here  m  is  the  number  of  grains  in  a  pound  =  7000,  and  /  is  the  number  of 
inches  in  a  foot  =  12  ;  /.  ml~B  =  7000/1  2s  =  4.051.  Hence  the  density  is  150  X 
4.051  =607.6  in  grains  per  cubic  inch. 

NOTE.  —  The  specific  gravity  of  a  body  is  the  ratio  of  its  density  to  the  density  of  a  standard 
substance.  The  dimension  formula  and  conversion  factor  are  therefore  both  unity. 

4.  Velocity.  —  The  velocity  of  a  body  at  any  instant  is  given  by  the  equation 
v  =  -p,  or  velocity  is  the  ratio  of  a  length-number  to  a  time-number.     The  di- 

d  r 

mension  formula  is  LT"1,  and  the  conversion  factor  lt~\ 

Example.  —  A  train  has  a  velocity  of  60  miles  an  hour  :  what  is  its  velocity  in 
feet  per  second  ? 


Here  7=5280  and  /  =  36oo  ;  .'.  trl  =  =  —  —  1-467.  Hence  the  velo- 
city =60  X  1-467  =  88.0  in  feet  per  second. 

5.  Angle.  —  An  angle  is  measured  by  the  ratio  of  the  length  of  an  arc  to  the 
length  of  the  radius  of  the  arc.     The  dimension  formula  and  the  conversion 
factor  are  therefore  both  unity. 

6.  Angular  Velocity.  —  Angular  velocity  is  the  ratio  of  the  magnitude  of  the 
angle  described  in  an  interval  of  time  to  the  length  of  the  interval.     The  dimen- 
sion formula  is  therefore  T"1,  and  the  conversion  factor  is  t~\ 

7.  Linear  Acceleration.  —  Acceleration  is  the  rate  of  change  of  velocity  or 

a  =  -?•     The  dimension  formula  is  therefore  VT"1  or  LT~a,  and  the  conversion 
at 

factor  is  /r2. 

Example?  —  A  body  acquires  velocity  at  a  uniform  rate,  and  at  the  end  of  one 
minute  is  moving  at  the  rate  of  20  kilometres  per  hour  :  what  is  the  acceleration 
in  centimetres  per  second  per  second  ? 

Since  the  velocity  gained  was  20  kilometres  per  hour  in  one  minute,  the  accel- 
eration was  1  200  kilometres  per  hour  per  hour. 

Here/=iooooo  and  /=36oo;  /.  //~2=  100000/3600*  =  .00771,  and  there- 
fore acceleration  =^.007  7  1  X  1200  =  9.26  centimetres  per  second. 

8.  Angular  Acceleration.  —  Angular  acceleration  is  rate  of  change  of  angu- 


XX  INTRODUCTION. 

lar  velocity.    The  dimensional  formula  is  thus  angulayelocity  or  T~2,  and  the 
conversion  factor  /~2. 

9.  Solid  Angle.  —  A  solid  angle  is  measured  by  the  ratio  of  the  surface  of 
the  portion  of  a  sphere  enclosed  by  the  conical  surface  forming  the  angle  to  the 
square  of  radius  of  the  spherical  surface,  the  centre  of  the  sphere  being  at  the 

vertex  of  the  cone.     The  dimensional  formula  is  therefore  — ^  or  i,  and  hence 

l_i 

the  conversion  factor  is  also  i. 

10.  Curvature.  —  Curvature  is  measured  by  the  rate  of  change  of  direction  of 
the  curve  with  reference  to  distance  measured  along  the  curve  as  independent 

variable.     The  dimension  formula  is  therefore  .ang  G.  or  Lr1,  and  the  conversion 

length 

factor  is  l~\ 

11.  Tortuosity.  —  Tortuosity  is  measured  by  the  rate  of  rotation  of  the  tan- 
gent plane  round  the  tangent  to  the  curve  of  reference  when  length  along  the 

curve  is  independent  variable.     The  dimension  formula  is  therefore   - — ^—?  or 

length 

Lr1,  and  the  conversion  factor  is  l~l. 

12.  Specific  Curvature  of  a  Surface.  —  This  was  defined  by  Gauss  to  be» 
at  any  point  of  the  surface,  the  ratio  of  the  solid  angle  enclosed  by  a  surface 
formed  by  moving  a  normal  to  the  surface  round  the  periphery  of  a  small  area 
containing  the  point,  to  the  magnitude  of  the  area.     The  dimensional  formula  is 

therefore  solld  angle  Or  L~2,  and  the  conversion  factor  is  thus  /-* 
surface 

13.  Momentum.  —  This  is  quantity  of  motion  in  the  Newtonian  sense,  and  is, 
at  any  instant,  measured  by  the  product  of  the  mass-number  and  the  velocity- 
number  for  the  body. 

Thus  the  dimension  formula  is  MV  or  MLT"1,  and  the  conversion  factor  mlf~\ 
Example.  —  A  mass  of  10  pounds  is  moving  with  a  velocity  of  30  feet  per  sec- 
ond :  what  is  its  momentum  when  the  centimetre,  the  gramme,  and  the  second  are 
fundamental  units  ? 

Here  m  =  453-59,  /=  30.48,  and  /=  i ;  .*.  mtrl  =  453-59  X  30.48  =  13825. 
The  momentum  is  thus  13825  X  10  X  30  =  4 147  500. 

14.  Moment  of  Momentum.  —  The  moment  of  momentum  of  a  body  with 
reference  to  a  point  is  the  product  of  its  momentum-number  and  the  number 
expressing  the  distance  of  its  line  of  motion  from  the  point.     The  dimensional 
formula  is  thus  ML^T"1,  and  hence  the  conversion  factor  is  mPr1. 

15.  Moment  of  Inertia.  — The  moment  of  inertia  of  a  body  round  any  axis 
is  expressed  by  the  formula  ^mr*,  where  m  is  the  mass  of  any  particle  of  the  body 


INTRODUCTION.  Xxi 

and  r  its  distance  from  the  axis.  The  dimension  formula  for  the  sum  is  clearly 
the  same  as  for  each  element,  and  hence  is  ML2.  The  conversion  factor  is  there- 
fore mt*. 

16.  Angular  Momentum.  —  The  angular  momentum  of  a  body  round  any 
axis  is  the  product  of  the  numbers  expressing  the  moment  of  inertia  and  the 
angular  velocity  of  the  body.     The  dimensional  formula  and  the  conversion  fac- 
tor are  therefore  the  same  as  for  moment  of  momentum  given  above. 

17.  Force.  —  A  force  is  measured  by  the  rate  of  change  of  momentum  it  is 
capable  of  producing.     The  dimension  formulae  for  force   and  "time  rate  of 
change  of  momentum  "  are  therefore  the  same,  and  are  expressed  by  the  ratio 
of  momentum-number  to  time-number  or  MLT~2.     The  conversion  factor  is  thus 


NOTE.  —  When  mass  is  expressed  in  pounds,  length  in  feet,  and  time  in  seconds,  the  unit  force 
is  called  the  poundal.  When  grammes,  centimetres,  and  seconds  are  the  corresponding  units  the 
unit  of  force  is  called  the  dyne. 

Example.     Find  the  number  of  dynes  in  25  poundals. 

Here  m  =  453-59>  l  =  3°-48,  and  t=  i  ;  .-.  m/r*=  453-59  X  30.48  —  13825 
nearly.  The  number  of  dynes  is  thus  13825  X  25  =345625  approximately. 

18.  Moment  of  a  Couple,  Torque,  or  Twisting  Motive.  —  These  are  dif- 
ferent names  for  a  quantity  which  can  be  expressed  as  the  product  of  two  numbers 
representing  a  force  and  a  length.     The  dimension  formula  is  therefore  FL  or 
ML2T~2,  and  the  conversion  factor  is  ml2*-*. 

19.  Intensity  of  a  Stress.  —  The  intensity  of  a  stress  is  the  ratio  of  the  num- 
ber expressing  the  total  stress  to  the  number  expressing  the  area  over  which  the 
stress  is  distributed.     The  dimensional  formula  is  thus  FLr2  or  ML"1'!"2,  and  the 
conversion  factor  is  ml~lt~*. 

20.  Intensity  of  Attraction,  or  "  Force  at  a  Point."  —  This  is  the  force  of 
attraction  per  unit  mass  on  a  body  placed  at  the  point,  and  the  dimensional  for- 
mula is  therefore  FM"1  or  LT~2,  the  same  as  acceleration.     The  conversion  fac- 
tors for  acceleration  therefore  apply. 

21.  Absolute  Force  of  a  Centre  of  Attraction,  or  "  Strength  of  a  Cen- 
tre." —  This  is  the  intensity  of  force  at  unit  distance  from  the  centre,  and  is  there- 
fore the  force  per  unit  mass  at  any  point  multiplied  by  the  square  of  the  distance 
from  the  centre.    The  dimensional  formula  thus  becomes  FL2M~J  or  L8T~2.    The 
conversion  factor  is  therefore  T8/"2. 

22.  Modulus  of  Elasticity.  —  A  modulus  of  elasticity  is  the  ratio  of  stress 
intensity  to  percentage  strain.     The  dimension  of  percentage  strain  is  a  length 
divided  by  a  length,  and  is  therefore  unity.    Hence,  the  dimensional  formula  of  a 
modulus  of  elasticity  is  the  same  as  that  of  stress  intensity,  or  ML-1T~2,  and  the 
conversion  factor  is  thus  also  ml~lt~*. 


Xxii  INTRODUCTION. 

23.  "Work  and  Energy.  —  When  the  point  of  application  of  a  force,  acting  on 
a  body,  moves  in  the  direction  of  the  force,  work  is  done  by  the  force,  and  the 
amount  is  measured  by  the  product  of  the  force  and  displacement  numbers.    The 
dimensional  formula  is  therefore  FL  or  ML2T~2. 

The  work  done  by  the  force  either  produces  a  change  in  the  velocity  of  the  body 
or  a  change  of  shape  or  configuration  of  the  body,  or  both.  In  the  first  case  it 
produces  a  change  of  kinetic  energy,  in  the  second  a  change  of  potential  energy. 
The  dimension  formulae  of  energy  and  work,  representing  quantities  of  the  same 
kind,  are  identical,  and  the  conversion  factor  for  both  is  #z/2/~2. 

24.  Resilience.  —  This  is  the  work  done  per  unit  volume  of  a  body  in  distort- 
ing it  to  the  elastic  limit  or  in  producing  rupture.    The  dimension  formula  is  there- 
fore ML2T-2L~8  or  MI/^T-2,  and  the  conversion  factor 


25.  Power,  or  Activity.  —  Power  —  or,  as  it  is  now  very  commonly  called,  ac- 
tivity —  is  defined  as  the  time  rate  of  doing  work,  or  if  W  represent  work  and  P  power 

P  =  —  .     The  dimensional  formula  is  therefore  WT"1  or  ML'T-8,  and  the  con- 
dt 

version  factor  mPr*,  or  for  problems  in  gravitation  units  more  conveniently./?/"1, 
where  /stands  for  the  force  factor. 

Examples,     (a)  Find  the  number  of  gramme  centimetres  in  one  foot  pound. 
Here  the  units  of  force  are  the  attraction  of  the  earth  on  the  pound*  and 
the  gramme  of  matter,  and  the  conversion  factor  is./7,  where/  is  453.59  and  /is 

30.48- 

Hence  the  number  is  453.59  X  30.48  =  13825. 

(ft)  Find  the  number  of  foot  poundals  in  i  oooooo  centimetre  dynes. 
Here  m  =  i/453-59>  '=  1/30.48,  and  /  =  i  ;  .-.  mt*r2  =  1/453-59  X  30.48', 
and  io6»i/»/-*=  107453.59  X  3°-482=  2.373. 

(c)  If  gravity  produces  an  acceleration  of  32.2  feet  per  second  per  second,  how 
many  watts  are  required  to  make  one  horse-power  ? 

One  horse-power  is  550  foot  pounds  per  second,  or  550X32.2  =  17710  foot 
poundals  per  second.  One  watt  is  io7  ergs  per  second,  that  is,  io7  dyne  centi- 
metres per  second.  The  conversion  factor  is  mf*t~s,  where  m  =  453-59>  ^=  3°-48, 
and  /=  i,  and  the  result  has  to  be  divided  by  io7,  the  number  of  dyne  centime- 
tres per  second  in  the  watt. 

Hence,  17710  mZ*r*/iol  =  17710  X  453-59  X  30.487  io7  =  746.3. 

(//)  How  many  gramme  centimetres  per  second  correspond  to  33000  foot 
pounds  per  minute  ? 

The  conversion  factor  suitable  for  this  case  is./?/""1,  where/  is  453-59>  '  is  30.48, 
and  /  is  60. 

Hence,  33000  //~1=  33000  X  453-59  X  30.48/60=  7604000  nearly. 

*  It  is  important  to  remember  that  in  problems  like  that  here  given  the  term  "pound"  or 
"  gramme  "  refers  to  force  and  not  to  mass. 


INTRODUCTION.  XX111 


HEAT  UNITS. 

i.  If  heat  be  measured  in  dynamical  units  its  dimensions  are  the  same  as  those 
of  energy,  namely  ML2T~2.  The  most  common  measurements,  however,  are 
made  in  thermal  units,  that  is,  in  terms  of  the  amount  of  heat  required  to  raise 
the  temperature  of  unit  mass  of  water  one  degree  of  temperature  at  some  stated 
temperature.  This  method  of  measurement  involves  the  unit  of  mass  and  some 
unit  of  temperature  ;  and  hence,  if  we  denote  temperature-numbers  by  ®  and  their 
conversion  factors  by  0,  the  dimensional  formula  and  conversion  factor  for  quan- 
tity of  heat  will  be  M©  and  mO  respectively.  The  relative  amount  of  heat  com- 
pared with  water  as  standard  substance  required  to  raise  unit  mass  of  different 
substances  one  degree  in  temperature  is  called  their  specific  heat,  and  is  a  simple 
number. 

Unit  volume  is  sometimes  used  instead  of  unit  mass  in  the  measurement  of 
heat,  the  units  being  then  called  thermometric  units.  The  dimensional  formula 
is  in  that  case  changed  by  the  substitution  of  volume  for  mass,  and  becomes  L8@, 
and  hence  the  conversion  factor  is  to  be  calculated  from  the  formula  1*6. 

For  other  physical  quantities  involving  heat  we  have :  — 


2.  Coefficient  of  Expansion.  —  The  coefficient  of  expansion  of  a  substance 
is  equal  to  the  ratio  of  the  change  of  length  per  unit  length  (linear),  or  change 
of  volume  per  unit  volume  (voluminal)  to  the  change  of  temperature.     These 
ratios  are  simple  numbers,  and  the  change  of  temperature  is  inversely  as  the  mag- 
nitude of  the  unit  of  temperature.     Hence  the  dimensional  and  conversion-factor 
formulae  are  ®-1  and  6~1. 

3.  Conductivity,  or  Specific  Conductance.  —  This  is  the  quantity  of  heat 
transmitted  per  unit  of  time  per  unit  of  surface  per  unit  of  temperature  gradient. 
The  equation  for  conductivity  is  therefore,  with  H  as  quantity  of  heat, 


and  the  dimensional  formula  7^r^  =  ^-^,  which  gives  ml~lf~l  for  conversion  factor. 


In  thermometric  units  the  formula  becomes  L^T"1,  which  properly  represents 
diffusivity.  In  dynamical  units  H  becomes  ML2T~2,  and  the  formula  changes  to 
MLT-8®-1.  The  conversion  factors  obtained  from  these  are  72/"1  and 
respectively. 


XXIV  INTRODUCTION. 

4.  Thermal  Capacity.  —  This  is  the  product  of  the  number  for  mass  and 
the  specific  heat,  and  hence  the  dimensional  formula  and  conversion  factor  are 
simply  M  and  m. 

5.  Latent  Heat.  —  Latent  heat  is  the  ratio  of  the  number  representing  the 
quantity  of  heat  required  to  change  the  state  of  a  body  to  the  number  represent- 
ing the  quantity  of  matter  in  the  body.     The  dimensional  formula  is  therefore 
M®/M  or  0,  and  hence  the  conversion  factor  is  simply  the  ratio  of  the  tempera- 
ture units  or  0.     In  dynamical  units  the  factor  is  /2/~2.* 

6.  Joule's  Equivalent.  —  Joule's  dynamical  equivalent  is  connected  with 
quantity  of  heat  by  the  equation 

ML2T-2  =  JHorJM®. 

This  gives  for  the  dimensional  formula  of  J  the  expression  U*T~*&~1.  The  conver- 
sion factor  is  thus  represented  by  /V"8^"1.  When  heat  is  measured  in  dynamical 
units  J  is  a  simple  number. 

7.  Entropy.  —  The  entropy  of  a  body  is  directly  proportional  to  the  quantity 
of  heat  it  contains  and  inversely  proportional  to  its  temperature.     The  dimen- 
sional formula  is  thus  M®/®  or  M,  and  the  conversion  factor  is  m.    When  heat  is 
measured  in  dynamical  units  the  factor  is  mlzt~^6~l. 

Examples,  (a)  Find  the  relation  between  the  British  thermal  unit,  the  calorie, 
and  the  therm. 

Neglecting  the  variation  of  the  specific  heat  of  water  with  temperature,  or  de- 
fining all  the  units  for  the  same  temperature  of  the  standard  substance,  we  have 
the  following  definitions.  The  British  thermal  unit  is  the  quantity  of  heat  required 
to  raise  the  temperature  of  one  pound  of  water  i°  F.  The  calorie  is  the  quan- 
tity of  heat  required  to  raise  the  temperature  of  one  kilogramme  of  water  i°  C. 
The  therm  is  the  quantity  of  heat  required  to  raise  the  temperature  of  one  gramme 
of  water  i°  C.  Hence :  — 

(1)  To  find  the  number  of  calories  in  one  British  thermal  unit,  we   have 
»*— 45399  and  0  =  f ;  .'•  w<9  =  . 45399  X  5/9—25199. 

(2)  To   find   the   number   of   therms   in   one   calorie,  m=iooo  and  6=1; 
.*.  mO=  1000. 

It  follows  at  once  that  the  number  of  therms  in  one  British  thermal  unit  is 
1000  X  .25199  =  251.99. 

(£)  What  is  the  relation  between  the  foot  grain  second  Fahrenheit-degree  and 
the  centimetre  gramme  second  Centigrade-degree  units  of  conductivity  ? 

The  number  of  the  latter  units  in  one  of  the  former  is  given  by  the  for- 

*  It  will  be  noticed  that  when  <=>  is  given  the  dimension  formula  L2T~2  the  formulae  in^  thermal 
and  dynamical  units  are  always  identical.  The  thermometric  units  practically  suppress  mass. 


INTRODUCTION.  XXV 

mula  ml~lt~l6°j  where  m  —  .  064  799,  /=  30.48,  and  /=  i,  and  is  therefore  = 
.064799/30.48  =  2.126  X  io~8. 

(c)  Find  the  relation  between  the  units  stated  in  (ft)  for  emissivity. 
In  this   case  the  conversion  formula  is  w/"2/""1,  where  ml  and  /  have  the 
same  value  as  before.     Hence  the  number  of  the  latter  units  in  the  former  is 
2  =  6.975  X  io~6. 


(d)  Find  the  number  of  centimetre  gramme  second  units  in  the  inch  grain 
hour  unit  of  emissivity. 

Here  the  formula  is  ml~*t~l,  where  m  —  0.064  799»  ^=2.54,  and  ^  =  3600. 
Therefore  the  required  number  is  0.064  799/2-542  X  3600  =  2.790  X  io~*. 

(e)  If  Joule's  equivalent  be  776  foot  pounds  per  pound  of  water  per  degree 
Fahrenheit,  what  will  be  its  value  in  gravitation  units  when  the  metre,  the 
kilogramme,  aud  the  degree  Centigrade  are  units  ? 


The  conversion  factor  in  this  case  is  ,,_a  or  I0~l,  where  /  =  .3048  and 
ff-l  =  i.S-,  .'.  776  X  .3048  X  1.8  =  425.7. 

(/)  If  Joule's  equivalent  be  24832  foot  poundals  when  the  degree  Fahren- 
heit is  unit  of  temperature,  what  will  be  its  value  when  kilogramme  metre 
second  and  degree-Centigrade  units  are  used  ? 

The  conversion  factor  is  Pr*0~l,  where  /=  .3048,  t  =  i,  and  0~l  =  1.8  ; 

.-.  24832  x  r-r2d~l  =  24832  x  .3048'  x  1.8  =  4152.5. 

In  gravitation  units  this  would  give  4152.5/9.81  =  423.3. 


ELECTRIC  AND  MAGNETIC  UNITS. 

There  are  two  systems  of  these  units,  the  electrostatic  and  the  electromagnetic 
systems,  which  differ  from  each  other  because  of  the  different  fundamental  suppo- 
sitions on  which  they  are  based.  In  the  electrostatic  system  the  repulsive  force 
between  two  quantities  of  static  electricity  is  made  the  basis.  This  connects  force, 

quantity  of  electricity,  and  length  by  the  equation  /=a  22l, where  /  is  force,  a  a 

quantity  depending  on  the  units  employed  and  on  the  nature  of  the  medium,  q  and 
ql  quantities  of  electricity,  and  /  the  distance  between  q  and  qt.  The  magnitude  of 
the  force  /  for  any  particular  values  of  q,  qt  and  /  depends  on  a  property  of  the 
medium  across  which  the  force  takes  place  called  its  inductive  capacity.  The  in- 
ductive capacity  of  air  has  generally  been  assumed  as  unity,  and  the  inductive 
capacity  of  other  media  expressed  as  a  number  representing  the  ratio  of  the  induc- 
tive capacity  of  the  medium  to  that  of  air.  These  numbers  are  known  as  the  spe- 
cific inductive  capacities  of  the  media.  According  to  the  ordinary  assumption, 
then,  of  air  as  the  standard  medium,  we  obtain  unit  quantity  of  electricity  when 
in  the  above  equation  y  =  ?{,  and/,  a,  and  /  are  each  unity.  A  formal  definition 
is  given  below. 

In  the  electromagnetic  system  the  repulsion  between  two  magnetic  poles  or 


XXvi  INTRODUCTION. 

quantities  of  magnetism  is  taken  as  the  basis.    In  this  system  the  quantities  force, 
quantity  of  magnetism,  and  length  are  connected  by  an  equation  of  the  form 


where  m  and  mt  are  in  this  case  quantities  of  magnetism,  and  the  other  symbols 
have  the  same  meaning  as  before.  In  this  case  it  has  been  usual  to  assume  the 
magnetic  inductive  capacity  of  air  to  be  unity,  and  to  express  the  magnetic  induc- 
tive capacity  of  other  media  as  a  simple  number  representing  the  ratio  of  the  in- 
ductive capacity  of  the  medium  to  that  of  air.  These  numbers,  by  analogy  with 
specific  inductive  capacity  for  electricity,  might  be  called  specific  inductive  capac- 
ities for  magnetism.  They  are  usually  called  permeabilities.  {Vide  Thomson, 
"  Papers  on  Electrostatics  and  Magnetism,"  p.  484.)  In  this  case,  also,  like  that 
for  electricity,  the  unit  quantity  of  magnetism  is  obtained  by  making  m  =  mt,  and 
/,  a,  and  /  each  unity. 

In  both  these  cases  the  intrinsic  inductive  capacity  of  the  standard  medium  is 
suppressed,  and  hence  also  that  of  all  other  media.  Whether  this  be  done  or  not, 
direct  experiment  has  to  be  resorted  to  for  the  determination  of  the  absolute  val- 
ues of  the  units  and  the  relations  of  the  units  in  the  one  system  to  those  in  the 
other.  The  character  of  this  relation  can  be  directly  inferred  from  the  dimen- 
sional formulae  of  the  different  quantities,  but  these  can  give  no  information  as  to 
the  relative  absolute  values  of  the  units  in  the  two  systems.  Prof.  Riicker  has 
suggested  (Phil.  Mag.  vol.  27)  the  advisability  of  at  least  indicating  the  exist- 
ence of  the  suppressed  properties  by  putting  symbols  for  them  in  the  dimensional 
formulae.  This  has  the  advantage  of  showing  how  the  magnitudes  of  the  different 
units  would  be  affected  by  a  change  in  the  standard  medium,  or  by  making  the 
standard  medium  different  for  the  two  systems.  In  accordance  with  this  idea,  the 
symbols  K  and  P  have  been  introduced  into  the  formulae  given  below  to  represent 
inductive  capacity  in  the  electrostatic  and  the  electromagnetic  systems  respectively. 
In  the  conversion  formulae  k  and/  are  the  ordinary  specific  inductive  capacities 
and  permeabilities  of  the  media  when  air  is  taken  as  the  standard,  or  generally 
those  with  reference  to  the  first  medium  taken  as  standard.  The  ordinary  for- 
mulae may  be  obtained  by  putting  K  and  P  equal  to  unity. 


ELECTROSTATIC   UNITS. 

i.  Quantity  of  Electricity.  —  The  unit  quantity  of  electricity  is  defined  as 
that  quantity  which  if  concentrated  at  a  point  and  placed  at  unit  distance  from  an 
equal  and  similarly  concentrated  quantity  repels  it,  or  is  repelled  by  it,  with  unit 
force.  The  medium  or  dielectric  is  usually  taken  as  air,  and  the  other  units  in  ac- 
cordance with  the  centimetre  gramme  second  system. 

In  this  case  we  have  the  force  of  repulsion  proportional  directly  to  the  square 
of  the  quantity  of  electricity  and  inversely  to  the  square  of  the  distance  between 
the  quantities  and  to  the  inductive  capacity.  The  dimensional  formula  is  there- 
fore the  same  as  that  for  [force  X  length2  X  inductive  capacity]*  or 
and  the  conversion  factor  is 


INTRODUCTION.  XXVii 

2.  Electric  Surface  Density  and  Electric  Displacement.  —  The  density 
of  an  electric  distribution  at  any  point  on  a  surface  is  measured  by  the  quantity 
per  unit  of  area,  and  the  electric  displacement  at  any  point  in  a  dielectric  is  mea- 
sured by  the  quantity  displaced  per  unit  of  area.    These  quantities  have  therefore 
the  same  dimensional  formula,  namely,  the  ratio  of  the  formulae  for  quantity  of 
electricity  and  for  area  or  M^Lr^T^K*,  and  the  conversion  factor  m*l~lt-l$. 

3.  Electric  Force  at  a  Point,  or  Intensity  of  Electric  Field.  —  This  is 
measured  by  the  ratio  of  the  magnitude  of  the  force  on  a  quantity  of  electricity  at 
a  point  to  the  magnitude  of  the  quantity  of  electricity.     The  dimensional  formula 
is  therefore  the  ratio  of  the  formulae  for  force  and  electric  quantity,  or 


which  gives  the  conversion  factor 

4.  Electric  Potential  and  Electromotive  Force.  —  Change  of  potential 
is  proportional  to  the  work  done  per  unit  of  electricity  in  producing  the  change. 
The  dimensional  formula  is  therefore  the  ratio  of  the  formulae  for  work  and  elec- 
tric quantity,  or 


which  gives  the  conversion  factor 

5.  Capacity  of  a  Conductor.  —  The  capacity  of  an  insulated  conductor  is 
proportional  to  the  ratio  of  the  numbers  representing  the  quantity  of  electricity  in 
a  charge  and  the  potential  of  the  charge.     The  dimensional  formula  is  thus  the 
ratio  of  the  two  formulae  for  electric  quantity  and  potential,  or 

*  _  T  K 

-* 

which  gives  Ik  for  conversion  factor.    When  K  is  taken  as  unity,  as  in  the  ordinary 
units,  the  capacity  of  an  insulated  conductor  is  simply  a  length. 

6.  Specific  Inductive  Capacity.  —  This  is  the  ratio  of  the  inductive  capac- 
ity of  the  substance  to  that  of  a  standard  substance,  and  hence  the  dimensional 
formula  is  K/K  or  i.* 

7.  Electric  Current.  —  Current  is  quantity  flowing  past  a  point  per  unit  of 
time.    The  dimensional  formula  is  thus  the  ratio  of  the  formulae  for  electric  quan- 
tity and  for  time,  or 


and  the  conversion  factor 

*  According  to  the  ordinary  definition  referred  to  air  as  standard  medium,  the  specific  inductive 
capacity  of  a  substance  is  K,  or  is  identical  in  dimensions  with  what  is  here  taken  as  inductive  ca- 
pacity. Hence  in  that  case  the  conversion  factor  must  be  taken  as  i  on  the  electrostatic  and  as 
on  the  electromagnetic  system. 


XXV111  INTRODUCTION. 

8.  Conductivity,  or  Specific*  Conductance.  —  This,  like  the  corresponding 
term  for  heat,  is  quantity  per  unit  area  per  unit  potential  gradient  per  unit  of  time. 
The  dimensional  formula  is  therefore 


__  ,p_1K  or 
""  * 


electric  quantity 


_ 
jj-,  area  X  potential  gradient  X  time 

~~ 


The  conversion  factor  is 

9.  Specific  *  Resistance.  —  This  is  the  reciprocal  of  conductivity  as  above 
defined,  and  hence  the  dimensional  formula  and  conversion  factor  are  respec- 
tively TK.-1  and  tk~\ 

10.  Conductance.  —  The  conductance  of  any  part  of  an  electric  circuit,  not 
containing  a  source  of  electromotive  force,  is  the  ratio  of  the  numbers  represent- 
ing the  current  flowing  through  it  and  the  difference  of  potential  between  its  ends. 
The  dimensional  formula  is  thus  the  ratio  of  the  formulae  for  current  and  poten- 
tial, or 


from  which  we  get  the  conversion  factor 

n.  Resistance.  —  This  is  the  reciprocal  of  conductance,  and  therefore  the 
dimensional  formula  and  the  conversion  factor  are  respectively  L^TK^1  and 


EXAMPLES   OF   CONVERSION    IN    ELECTROSTATIC   UNITS. 

(a)  Pind  the  factor  for  converting  quantity  of  electricity  expressed  in  foot  grain 
second  units  to  the  same  expressed  in  c.  g.  s.  units. 

By  (i)  the  formula  is  wV3/"1^,  in  which  in  this  case  m  =  0.0648,  /=  30.48,  /  = 
i,  and  k  =  i ;  .*.  the  factor  is  0.0648*  X  30.48*  =  4.2836. 

(£)  Find  the  factor  required  to  convert  electric  potential  from  millimetre  milli- 
gramme second  units  to  c.  g.  s.  units. 

By  (4)  the  formula  is  »/i/i/~1^"~J,  and  in  this  case  m  =  o.ooi,  /=  o.i,  /=  i,  and 
£=i;  .*.  the  factor  =  o.ooi1  X  o.ij=o.oi. 

(<:)  Find  the  factor  required  to  convert  from  foot  grain  second  and  specific  in- 
ductive capacity  6  units  to  c.  g.  s.  units. 

By  (5)  the  formula  is  /£,  and  in  this  case  7=30.48  and  £  =  6;  .*.  the  factor 
=  30.48  X  6  =  182.88. 

*  The  term  "  specific/'  as  used  here  and  in  9,  refers  conductance  and  resistance  to  that  between 
the  ends  of  a  bar  of  unit  section  and  unit  length,  and  hence  is  different  from  the  same  term  in 
specific  heat,  specific  inductivity,  capacity,  etc.,  which  refer  to  a  standard  substance. 


INTRODUCTION.  XXIX 


ELECTROMAGNETIC   UNITS. 

As  stated  above,  these  units  bear  the  same  relation  to  unit  quantity  of  magne- 
tism that  the  electric  units  do  to  quantity  of  electricity.  Thus,  when  inductive 
capacity  is  suppressed,  the  dimensional  formula  for  magnetic  quantity  on  this  sys- 
tem is  the  same  as  that  for  electric  quantity  on  the  electrostatic  system.  All  quan- 
tities in  this  system  which  only  differ  from  corresponding  quantities  defined  above 
by  the  substitution  of  magnetic  for  electric  quantity  may  have  their  dimensional 
formulae  derived  from  those  of  the  corresponding  quantity  by  substituting  P 
forK. 

i.  Magnetic  Pole,  or  Quantity  of  Magnetism.  —  Two  unit  quantities  of 
magnetism  concentrated  at  points  unit  distance  apart  repel  each  other  with  unit 
force.  The  dimensional  formula  is  thus  the  same  as  for  [force  X  length2  X  in- 
ductive capacity]  or  M^UT"1?1,  and  the  conversion  factor  is 


2.  Density  of  Surface  Distribution  of  Magnetism.  —  This  is  measured 
by  quantity  of  magnetism  per  unit  area,  and  the  dimension  formula  is  therefore 
the  ratio  of  the  expressions  for  magnetic  quantity  and  for  area,  or  MiLriT~1P}, 
which  gives  the  conversion  factor 


3.  Magnetic  Force  at  a  Point,  or  Intensity  of  Magnetic  Field.  —  The 
number  for  this  is  the  ratio  of  the  numbers  representing  the  magnitudes  of  the 
force  on  a  magnetic  pole  placed  at  the  point  and  the  magnitude  of  the  magnetic 
pole. 

The  dimensional  formula  is  therefore  the  ratio  of  the  expressions  for  force  and 
magnetic  quantity,  or 


MiJJT-lpi 

and  the  conversion  factor 


4.  Magnetic  Potential.  —  The  magnetic  potential  at  a  point  is  measured  by 
the  work  which  is  required  to  bring  unit  quantity  of  positive  magnetism  from  zero 
potential  to  the  point.  The  dimensional  formula  is  thus  the  ratio  of  the  formula 
for  work  and  magnetic  quantity,  or 


which  gives  the  conversion  factor 

5.  Magnetic  Moment.  —  This  is  the  product  of  the  numbers  for  pole 
strength  and  length  of  a  magnet.  The  dimensional  formula  is  therefore  the  pro- 
duct of  the  formulae  for  magnetic  quantity  and  length,  or  M^T"1?*,  and  the  con- 
version factor 


6.  Intensity  of  Magnetization.  —  The  intensity  of  magnetization  of  any  por- 
tion of  a  magnetized  body  is  the  ratio  of  the  numbers  representing  the  magni- 


XXX  INTRODUCTION. 


tude  of  the  magnetic  moment  of  that  portion  and  its  volume.     The  dimensional 
formula  is  therefore  the  ratio  of  the  formulae  for  magnetic  moment  and  volume,  or 


L 

The  conversion  factor  is  therefore 

7.  Magnetic  Permeability,*  or  Specific  Magnetic  Inductive  Capacity. 
—  This  is  the  analogue  in  magnetism  to  specific  inductive  capacity  in  electricity. 
It  is  the  ratio  of  the  magnetic  induction  in  the  substance  to  the  magnetic  induc- 
tion in  the  field  which  produces  the  magnetization,  and  therefore  its  dimensional 
formula  and  conversion  factor  are  unity. 

8.  Magnetic  Susceptibility.  —  This  is  the  ratio  of  the  numbers  which  repre- 
sent the  values  of  the  intensity  of  magnetization  produced  and  the  intensity  of  the 
magnetic  field  producing  it.     The  dimensional  formula  is  therefore  the  ratio  of 
the  formulae  for  intensity  of  magnetization  and  magnetic  field  or 

* 
* 

The  conversion  factor  is  therefore  /,  and  both  the  dimensional  formula  and  con- 
version factor  are  unity  in  the  ordinary  system. 

9.  Current  Strength.  —  A  current  of  strength  c  flowing  round  a  circle  of 
radius  r  produces  a  magnetic  field  at  the  centre  of  intensity  2Trcjr.     The  dimen- 
sional formula  is  therefore  the  product  of  the  formulae  for  magnetic  field  intensity 
and  length,  or  M^T"1?"*,  which  gives  the  conversion  factor 


10.  Current  Density,  or  Strength  of  Current  at  a  Point.  —  This  is  the 
ratio  of  the  numbers  for  current  strength  and  area.  The  dimensional  formula 
and  the  conversion  factor  are  therefore  M^L^T-1?-1  and 


ii.  Quantity  of  Electricity.  —  This  is  the  product  of  the  numbers  for  cur- 
rent and  time.  The  dimensional  formula  is  therefore  WL*T~lp-*  X  T=  MJL*P~*, 
and  the  conversion  factor 


12.  Electric  Potential,  or  Electromotive  Force.  —  As  in  the  electrostatic 
system,  this  is  the  ratio  of  the  numbers  for  work  and  quantity  of  electricity.  The 
dimensional  formula  is  therefore 


and  the  conversion  factor 

*  Permeability,  as  ordinarily  taken  with  the  standard  medium  as  unity,  has  the  same  dimension 
formula  and  conversion  factor  as  that  which  is  here  taken  as  magnetic  inductive  capacity.  Hence 
for  ordinary  transformations  the  conversion  factor  should  be  taken  as  I  in  the  electromagnetic  and 
j~2t2  in  the  electrostatic  systems. 


INTRODUCTION.  XXXI 


13.  Electrostatic  Capacity.  —  This  is  the  ratio  of  the  numbers  for  quantity 
of  electricity  and  difference  of  potential.     The  dimensional  formula  is  therefore 


and  the  conversion  factor 

14.  Resistance  of  a  Conductor.  —  The  resistance  of  a  conductor  or  elec- 
trode is  the  ratio  of  the  numbers  for  difference  of  potential  between  its  ends  and 
the  constant  current  it  is  capable  of  producing.  The  dimensional  formula  is 
therefore  the  ratio  of  those  for  potential  and  current  or 


The  conversion  factor  thus  becomes  #-1/,  and  in  the  ordinary  system  resistance 
has  the  same  conversion  factor  as  velocity. 

15.  Conductance.  —  This  is  the  reciprocal  of  resistance,  and  hence  the  dimen- 
sional formula  and  conversion  factor  are  respectively  Lr^TP"1  and 


16.  Conductivity,  or  Specific  Conductance.  —  This  is  quantity  of  electric- 
ity transmitted  per  unit  of  area  per  unit  of  potential  gradient  per  unit  of  time. 
The  dimensional  formula  is  therefore  derived  from  those  of  the  quantities  men- 
tioned as  follows  :  — 


L 

The  conversion  factor  is  therefore 


17.  Specific  Resistance.  —  This  is  the  reciprocal  of  conductivity  as  defined 
in  1 6,  and  hence  the  dimensional  formula  and  conversion  factor  are  respectively 
and 


18.  Coefficient  of  Self-induction,  or  Inductance,  or  Electro-kinetic  In- 
ertia. —  These  are  for  any  circuit  the  electromotive  force  produced  in  it  by  unit 
rate  of  variation  of  the  current  through  it.     The  dimensional  formula  is  therefore 
the  product  of  the  formulae  for  electromotive  force  and  time  divided  by  that  for 
current  or 

•»  rl-r  arn_o-r»l 

X  T  =  LP. 

The  conversion  factor  is  therefore  lp,  and  in  the  ordinary  system  is  the  same  as 
that  for  length. 

19.  Coefficient  of  Mutual  Induction.  —  The  mutual  induction  of  two  cir- 
cuits is  the  electromotive  force  produced  in  one  per  unit  rate  of  variation  of  the 
current  in  the  other.     The  dimensional  formula  and  the  conversion  factor  are 
therefore  the  same  as  those  for  self-induction. 


XXX11  INTRODUCTION. 


20.  Electro-kinetic  Momentum.  —  The  number  for  this  is  the  product  of 
the  numbers  for  current  and  for  electro-kinetic  inertia.  The  dimensional  formula 
is  therefore  the  product  of  the  formulae  for  these  quantities,  or  M^T"1?"*  X  LP 
=  M*UT-1P*,  and  the  conversion  factor  is 


21.  Electromotive  Force  at  a  Point.  —  The  number  for  this  quantity  is 
the  ratio  of  the  numbers  for  electric  potential  or  electromotive  force  as  given  in 
12,  and  for  length.  The  dimensional  formula  is  therefore  MiLiT~2PJ,  and  the 
conversion  factor 


22.  Vector  Potential.  —  This  is  time  integral  of  electromotive  force  at  a 
point,  or  the  electro-kinetic  momentum  at  a  point.  The  dimensional  formula 
may  therefore  be  derived  from  21  by  multiplying  by  T,  or  from  20  by  dividing 
by  L.  It  is  therefore  M*!,*!""1?*,  and  the  conversion  factor 


23.  Thermoelectric  Height.  —  This  is  measured  by  the  ratio  of  the  num- 
bers for  electromotive  force  and  for  temperature.  The  dimensional  formula  is 
therefore  the  ratio  of  the  formulae  for  these  two  quantities,  or  MiLiT~2Pi®~1,  and 
the  conversion  factor 


24.  Specific  Heat  of  Electricity.  —  This  quantity  is  measured  in  the  same 
way  as  23,  and  hence  has  the  same  formulas. 

25.  Coefficient  of  Peltier  Effect.  —  This  is  measured  by  the  ratio  of  the 
numbers  for  quantity  of  heat  and  for  quantity  of  electricity.     The  dimensional 
formula  is  therefore 


and  the  conversion  factor 


EXAMPLES   OF    CONVERSION    IN    ELECTROMAGNETIC   UNITS. 

(a)  Find  the  factor  required  to  convert  intensity  of  magnetic  field  from  foot 
grain  minute  units  to  c.  g.  s.  units. 

By  (3)  the  formula  is  w*/"*/"1/"*,  and  in  this  case  m  =  0.0648,  /=  30.48,  /  = 
60,  and/  =  i  ;  .*.  the  factors  =  0.0648*  X  30.48"*  X  6o~1  =  0.00076847. 

Similarly  to  convert  from  foot  grain  second  units  to  c.  g.  s.  units  the  factor  is 
0.0648*  X  30.48"*  =  0.046  1 08. 

(£)  How  many  c.  g.  s.  units  of  magnetic  moment  make  one  foot  grain  second 
unit  of  the  same  quantity  ? 

By  (5)  the  formula  is  #z*/*/~~^*,  and  the  values  for  this  problem  are  m  =  0.0648, 
/=  30.48,  t=  i,  and/  =  i  ;  .'.  the  number  =  0.0648*  X  30.48*=  1305.6. 

(c)  If  the  intensity  of  magnetization  of  a  steel  bar  be  700  in  c.  g.  s.  units,  what 
will  it  be  in  millimetre  milligramme  second  units  ? 


INTRODUCTION.  XXX111 


By  (6)  the  formula  is  wW"1/*,  and  in  this  case  m  =  1000,  /=  10,  /==  i,  and 
p  =  i  j  /.the  intensity  =  700  X  1000*  X  10*  =  70000. 

(d)  Find  the  factor  required  to  convert  current  strength  from  c.  g.  s.  units  to 
earth  quadrant  io~u  gramme  and  second  units. 

By  (9)  the  formula  is  mll}rlp~*,  and  the  values  of  these  quantities  are  here  m  = 
lo11,  /=  io~9,  /  =  i,  and/  =  i  ;  /.  the  factor  =  ioH  x  io~J  =  10. 

(e)  Find  the  factor  required  to  convert  resistance  expressed  in  c.  g.  s.  units  into 
the  same  expressed  in  earth-quadrant  io~u  grammes  and  second  units. 

By  (14)  the  formula  is  #~^,  and  for  this  case  /=  io~',  /=  i,  and  /  =  i  ; 
/.  the  factor  =  io~9. 

(/)  Find  the  factor  required  to  convert  electromotive  force  from  earth-quadrant 
io~n  gramme  and  second  units  to  c.  g.  s.  units. 

By  (12)  the  formula  is  f^*/8/"^*,  and  for  this  case  m  =  io~u,  /==  io9,  /=  i, 
and/  =  i  ;  .*.  the  factor  =  io8. 


PRACTICAL  UNITS. 

In  practical  electrical  measurements  the  units  adopted  are  either  multiples  or 
submultiples  of  the  units  founded  on  the  centimetre,  the  gramme,  and  the  second 
as  fundamental  units,  and  air  is  taken  as  the  standard  medium,  for  which  K  and  P 
are  assumed.unity.  The  following,  quoted  from  the  report  to  the  Honorable  the 
Secretary  of  State,  under  date  of  November  6th,  1893,  by  the  delegates  repre- 
senting the  United  States,  gives  the  ordinary  units  with  their  names  and  values 
as  defined  by  the  International  Congress  at  Chicago  in  1893  :  — 

"  Resolved,  That  the  several  governments  represented  by  the  delegates  of  this 
International  Congress  of  Electricians  be,  and  they  are  hereby,  recommended  to 
formally  adopt  as  legal  units  of  electrical  measure  the  following :  As  a  unit  of  re- 
sistance, the  international  ohm,  which  is  based  upon  the  ohm  equal  to  io9  units  of 
resistance  of  the  C.  G.  S.  system  of  electro-magnetic  units,  and  is  represented 
by  the  resistance  offered  to  an  unvarying  electric  current  by  a  column  of  mercury 
at  the  temperature  of  melting  ice  14.4521  grammes  in  mass,  of  a  constant  cross- 
sectional  area  and  of  the  length  of  106.3  centimetres. 

"  As  a  unit  of  current,  the  international  ampere,  which  is  one  tenth  of  the  unit  of 
current  of  the  C.  G.  S.  system  of  electro-magnetic  units,  and  which  is  represented 
sufficiently  well  for  practical  use  by  the  unvarying  current  which,  when  passed 
through  a  solution  of  nitrate  of  silver  in  water,  and  in  accordance  with  accom- 
panying specifications,*  deposits  silver  at  the  rate  of  0.001118  of  a  gramme  per 
second. 

*  "  In  the  following  specification  the  term  '  silver  voltameter '  means  the  arrangement  of  appara- 
tus by  means  of  which  an  electric  current  is  passed  through  a  solution  of  nitrate  of  silver  in  water. 
The  silver  voltameter  measures  the  total  electrical  quantity  which  has  passed  during  the  time  of 
the  experiment,  and  by  noting  this  time  the  time  average  of  the  current,  or,  if  the  current  has  been 
kept  constant,  the  current  itself  can  be  deduced. 

"  In  employing  the  silver  voltameter  to  measure  currents  of  about  one  ampere,  the  following 
arrangements  should  be  adopted :  — 


XXXIV  INTRODUCTION. 

"  As  a  unit  of  electromotive  force,  the  international  volt,  which  is  the  electro- 
motive force  that,  steadily  applied  to  a  conductor  whose  resistance  is  one  interna- 
tional ohm,  will  produce  a  current  of  one  international  ampere,  and  which  is  rep- 
resented sufficiently  well  for  practical  use  by  T$§£  of  the  electromotive  force 
between  the  poles  or  electrodes  of  the  voltaic  cell  known  as  Clark's  cell,  at  a  tem- 
perature of  15°  C.,  and  prepared  in  the  manner  described  in  the  accompanying 
specification.* 

"  As  a  unit  of  quantity,  the  international  coulomb,  which  is  the  quantity  of  elec- 
tricity transferred  by  a  current  of  one  international  ampere  in  one  second. 

"As  a  unit  of  capacity,  the  international  farad,  which  is  the  capacity  of  a  con- 
denser charged  to  a  potential  of  one  international  volt  by  one  international  cou- 
lomb of  electricity. t 

"  As  a  unit  of  work,  the  joule,  which  is  equal  to  io7  units  of  work  in  the  c.  g.  s. 
system,  and  which  is  represented  sufficiently  well  for  practical  use  by  the  energy 
expended  in  one  second  by  an  international  ampere  in  an  international  ohm. 

"As  a  unit  of  power,  the  watt,  which  is  equal  to  io7  units  of  power  in  the  c.  g.  s. 
system,  and  which  is  represented  sufficiently  well  for  practical  use  by  the  work 
done  at  the  rate  of  one  joule  per  second. 

"  As  the  unit  of  induction,  the  henry,  which  is  the  induction  in  a  circuit  when 
the  electromotive  force  induced  in  this  circuit  is  one  international  volt,  while  the 
inducing  current  varies  at  the  rate  of  one  ampere  per  second. 

"  The  Chamber  also  voted  that  it  was  not  wise  to  adopt  or  recommend  a  stand- 
ard of  light  at  the  present  time." 

By  an  Act  of  Congress  approved  July  i2th,  1894,  the  units  recommended  by 
the  Chicago  Congress  were  adopted  in  this  country  with  only  some  unimportant 
verbal  changes  in  the  definitions. 

By  an  Order  in  Council  of  date  August  23d,  1894,  the  British  Board  of  Trade 
adopted  the  ohm,  the  ampere,  and  the  volt,  substantially  as  recommended  by 
the  Chicago  Congress.  The  other  units  were  not  legalized  in  Great  Britain. 
They  are,  however,  in  general  use  in  that  country  and  all  over  the  world. 

"  The  kathode  on  which  the  silver  is  to  be  deposited  should  take  the  form  of  a  platinum  bowl 
not  less  than  io  centimetres  in  diameter  and  from  4  to  5  centimetres  in  depth. 

"  The  anode  should  be  a  plate  of  pure  silver  some  30  square  centimetres  in  area  and  2  or  3 
millimetres  in  thickness. 

"  This  is  supported  horizontally  in  the  liquid  near  the  top  of  the  solution  by  a  platinum  wire 
passed  through  holes  in  the  plate  at  opposite  corners.  To  prevent  the  disintegrated  silver  which 
is  formed  on  the  anode  from  falling  on  to  the  kathode,  the  anode  should  be  wrapped  round  with 
pure  filter  paper,  secured  at  the  back  with  sealing  wax. 

"The  liquid  should  consist  of  a  neutral  solution  of  pure  silver  nitrate,  containing  about  15  parts 
by  weight  of  the  nitrate  to  85  parts  of  water. 

"  The  resistance  of  the  voltameter  changes  somewhat  as  the  current  passes.  To  prevent  these 
changes  having  too  great  an  effect  on  the  current,  some  resistance  besides  that  of  the  voltameter 
should  be  inserted  in  the  circuit.  The  total  metallic  resistance  of  the  circuit  should  not  be  less 
than  io  ohms." 

*  A  committee,  consisting  of  Messrs.  Helmholtz,  Ayrton,  and  Carhart,  was  appointed  to  pre- 
pare specifications  for  the  Clark's  cell,  but  no  report  was  made,  on  account  of  Helmholtz's  death. 

t  The  one  millionth  part  of  the  farad  is  more  commonly  used  in  practical  measurements,  and  is 
called  the  microfarad. 


PHYSICAL  TABLES 


T  ABLE  1  . 

FUNDAMENTAL  AND  DERIVED  UNITS, 


To  change  a  quantity  from  one  system  of  units  to  another  :  substitute  in  the  correspond- 
ing conversion  factor  from  the  following  table  the  ratio  of  the  magnitudes  of  the  old  units 
to  the  new  and  multiply  the  old  quantity  by  the  resulting  number.  For  example  :  to  reduce 
velocity  in  miles  per  hour  to  feet  per  second,  the  conversion  factor  is  //—1;  /=528o/i, 
/=36oo/i,  therefore  the  factor=528o/36oo=i.467. 


(a)  FUNDAMENTAL  UNITS. 


Name  of  Unit. 


Symbol. 


Conversion  Factor. 


Length. 

Mass. 

Time. 

Temperature. 

Electric  Inductive  Capacity. 

Magnetic  Inductive  Capacity. 


L 

M 
T 
© 
K 
P 


(£)  DERIVED  UNITS. 
I.    Geometric  and  Dynamic  Units. 


Name  of  Unit. 


Conversion  Factor. 


Area. 
Volume. 
Angle. 
Solid  Angle. 
Curvature. 
Tortuosity. 

Specific  curvature  of  a  surface. 
Angular  velocity. 
Angular  acceleration. 
Linear  velocity. 
Linear  acceleration. 
Density. 

Moment  of  inertia. 

Intensity  of  attraction,  or  "  force  at  a  point." 
Absolute  force  of  a  centre  of  attraction,  or  "  strength ") 
of  a  centre."  ) 

Momentum. 

Moment  of  momentum,  or  angular  momentum. 
Force. 

Moment  of  a  couple,  or  torque. 
Intensity  of  stress. 
Modulus  of  elasticity. 
Work  and  energy. 
Resilience. 
Power  or  activity. 


//~2 

w/2 
//~2 


mtr1 
mtr* 


m  /-1  /-' 


SMITHSONIAN  TABLES. 


TABLE  1 . 
FUNDAMENTAL  AND  DERIVED  UNITS. 


//.   Heat  Units. 


Name  of  Unit. 


Conversion  Factor. 


Quantity  of  heat  (thermal  units). 

"     (thermometric  units). 
"  "     (dynamical  units). 

Coefficient  of  thermal  expansion. 
Conductivity  (thermal  units). 

f  thermometric  units),  or  diffusivity. 
"  (dynamical  units). 

Thermal  capacity. 
Latent  heat  (thermal  units). 

"         "     (dynamical  units). 
Joule's  equivalent. 

Entropy  (heat  measured  in  thermal  units). 
"        (   "  "         "  dynamical  units). 


mO 
1*0 


m 


III.   Magnetic  and  Electric  Units. 


Name  of  Unit. 


Conversion  factor 
for  electrostatic 
system. 


Conversion  factor 
for  electromag- 
netic system. 


Magnetic  pole,  or  quantity  of  mag- 
netism. 

Density  of  surface  distribution  of 
magnetism. 

Intensity  of  magnetic  field. 

Magnetic  potential. 

Magnetic  moment. 

Intensity  of  magnetisation. 

Magnetic  permeability. 

Magnetic   susceptibility  and    mag-) 
netic  inductive  capacity.  j 

Quantity  of  electricity. 

Electric  surface  density  and  electric  ) 


/>  r1/1 


n 


«*/' 

m*ll 


displacement. 
Intensity  of  electric  field. 
Electric  potential  and  e.  m.  f. 
Capacity  of  a  condenser. 
Inductive  capacity. 
Specific  inductive  capacity. 
Electric  current. 


m*l* 

Ik 

k 

i 

m*l* 


t-^k-* 


r*# 


nj>  /-I/ 
*»/* 


SMITHSONIAN  TABLES. 


TABLE  1. 
FUNDAMENTAL  AND  DERIVED  UNITS. 


///.   Magnetic  and  Electric  Units. 

Conversion  factor 

Conversion  factor 

Name  of  Unit. 

for  electrostatic 

for  electromag- 

system. 

netic  system. 

Conductivity. 
Specific  resistance. 

jj* 

wy 

Conductance. 

1  1~^  k 

f~i  t  p~i 

Resistance. 

t*tK+ 

i  t~i  p 

Coefficient  of  self    induction    and) 

^  .   2  t-i 

7  -A 

coefficient  of  mutual  induction,      j 

rrr  k 

IP 

Electrokinetic  momentum. 

m\  l\  £-* 

m*  I*  rlp* 

Electromotive  force  at  a  point. 

m\  /-*  /-I  £-i 

m*  /l  /~2/* 

Vector  potential. 

fffi  /~i  k~* 

m*  /*  r"1/* 

Thermoelectric  height  and  specific) 
heat  of  electricity.                            j" 

*flr*ir*** 

*>>  /'  rv»  «-* 

Coefficient  of  Peltier  effect. 

m*  f*  t  IT*  6 

SMITHSONIAN  TABLES. 


TABLE  2. 
TABLES  FOR  CONVERTING  U.  S.  WEIGHTS  AND  MEASURES.* 

(1)   CUSTOMARY  TO   METRIC. 


,                        LINEAR. 

CAPACITY. 

Inches 
to 
millimetres. 

Feet  to 

metres. 

Yards  to 
metres. 

Miles 
to 
kilometres. 

Fluid 
drams  to 
millilitres 
or  cubic 

Fluid 
ounces 
to 

Liquid 
quarts  to 
litres. 

Gallons  to 
litres. 

centimetres. 

•ft 

25.4001 

0.304801 

0.914402 

1.60935 

i 

3-70 

29-57 

0.94636 

378543 

2 

50.8001 

0.60960! 

1.828804 

3.21869 

2 

7-39 

59-  *  5 

1.89272 

7.57087 

3 

76.2002 

0.914402 

2.743205 

4.82804 

3 

11.09 

88.72 

2.83908 

11.35630 

4 

IOI.6002 

1.219202 

3.657607 

6-43739 

4 

14.79 

118.29 

378543 

15.14174 

5 

127.0003 

1.524003 

4.572009 

8.04674 

5 

18.48 

147.87 

18.92717 

6 

i 

9 

152.4003 
177.8004 
203.2004 
228.6005 

1.828804 
2.133604 
2.438405 
2.743205 

5.48641  1 
6.400813 

7-3I52I5 
8.229616 

9.65608 
11.26543 
12.87478 
14.48412 

6 

I 

9 

22.18 
25.88 
29.57 
33.27 

177-44 
207.02 

236.59 
266.16 

5.67815 
6.62451 
7.57087 
8.51723 

22.71261 
26.49804 
30-28348 
34.06891 

SQUARE. 

WEIGHT. 

Square 
inches  to 
square  cen- 
timetres. 

Square  feet 
to  square 
decimetres. 

Square 
yards  to 
square 
metres. 

Acres  to 
hectares. 

Grains  to 

milli- 
grammes. 

Avoirdu- 
pois ounces 
to 
grammes. 

Avoirdu- 
pois pounds 
to  kilo- 
grammes. 

Troy 
ounces  to 
grammes. 

6.452 
12.903 

ifc?? 

0.836 
1.672 

0.4047 
0.8094 

i 

2 

64.7989 
129.5978 

28.3495 
$6.6991 

0-45359 
0.90718 

•  31.10348 
62.20696 

J9-355 
25.807 

32.258 

27.871 
37.161 
46.452 

2.508 

3-345 
4.181 

1.2141 
1.6187 
2.0234 

3 

4 

5 

194.3968 

2  59-  !  957 

323.9946 

85.0486 
113.3981 
141.7476 

1.36078 

I.8I437 
2.26796 

93-3  !  044 
124.41392 

38.710 
45.161 

55-742 
65.032 

5-o  1  7 
5-853 

2.4281 
2.8328 

6 

7 

388.7935 
453-5924 

170.0972 
198.4467 

2.72I55 

186.62088 
217.72437 

51.613 
58.065 

74-323 
83-613 

6.689 

7.525 

3-2375 
3.6422 

8 
9 

583-1903 

226.7962 
255-H57 

3-62874 
4.08233 

248.82785 

279.93  *  33 

CUBIC. 

Cubic 
inches  to 
cubic  cen- 
timetres. 

Cubic  feet 
to  cubic 
metres. 

Cubic 
yards  to 
cubic 
metres. 

Bushels  to 
hectolitres. 

i  Gunter's  chain  =     20.1168          metres, 
i  sq.  statute  mile  =    259.000          hectares. 

i  fathom                =        1.829            metres. 

16.387 

0.02832 

0.765 

0.35239 

i  nautical  mile     =  1853.25              metres. 

32.774 

0.05663 

1-529 

0.70479 

i  foot                    =        0.304801        metre. 

49.161 
65.549 

0.08495 
0.11327 

2.294 
3.058 

1.05718 
1.40957 

i  avoir,  pound      =    453.5924277  grammes. 

5 

81.936 

0.14159 

3.823 

1.76196 

1  5432.35639  grains  =       i.ooo    kilogramme. 

6 

98.323 

0.16990 

4.587 

2.11436 

7 

II47IO 

0.19822 

5-352 

2.46675 

8 

131.097 

0.22654 

6.II6 

2.81914 

9 

147.484 

0.25485 

6.881 

3.I7I54 

According  to  an  executive  order  dated  April  15,  1893,  the  United  States  yard  is  defined  as  3600/3937  metre,  and 
the  avoirdupois  pound  as  1/2.20462  kilogramme. 

The  only  authorized  material  standard  of  customary  weight  is  the  Troy  pound  of  the  Mint.  It  is  of  brass  of  un- 
known density,  and  therefore  not  suitable  for  a  standard  of  mass.  It  was  derived  from  the  British  standard  Troy 
pound  of  1758  by  direct  comparison. 

The  British  gallon  =  4.5459631  litres. 

The  British  bushel  =  36.3477  litres. 

The  length  of  the  nautical  mile  given  above  and  adopted  by  the  U.  S.  Coast  and  Geodetic  Survey  many  years  ago, 
is  defined  as  that  of  a  minute  of  arc  of  a  great  circle  of  a  sphere  whose  surface  equals  that  of  the  earth  (Clarke's  Sphe- 
roid of  1866). 

*  Quoted  from  sheets  issued  by  the  United  States  Bureau  of  Standards. 
SMITHSONIAN  TABLES. 


TABLE  2. 
TABLES  FOR  CONVERTING  U.  S.  WEIGHTS  AND  MEASURES. 

(2)   METRIC  TO  CUSTOMARY. 


LINEAR. 

CAPACITY. 

Millilitres 

or  cubic 

Centi- 

Deca 

Hecto- 

Metres to 

Metres  to 

Metres  to 

Kilometres 

centi- 

litres to 

litres 

litres 

inches. 

feet. 

yards. 

to  miles. 

metres 

fluid 

to 

to 

to  fluid 

ounces. 

gallons. 

bushels. 

drams. 

I 
2 

39-3700 
78.7400 

6.56167 

1.093611 
2.187222 

0.62137 
1.24274 

I 

2 

0.27 

0.676 

1.0567 
2.1134 

2.6417 

2.8377 
5-6755 

3 
4 
5 

118.1100 
157.4800 
196.8500 

9.84250 

I3-I2333 
16.40417 

3-280833 
4.374444 
5.468056 

1.86411 
2.48548 
3-I0685 

3 
4 

5 

?!o8 

1.014 

1-353 
1.691 

3.1700 
4.2267 

7-9251 
10.5668 
13.2085 

8.5132 
H.35'0 

14.1887 

6 

I 

236.2200 
275.5900 
314.9600 

19.68500 
22.96583 
26.24667 

6.561667 
7-655278 
8.748889 

3.72822 

4-34959 
4.97096 

6 
8 

1.62 
1.89 
2.l6 

2.029 
2.367 
2.705 

6.3401 
7-3968 

8-4535 

1  5.8502 
18.4919 
21.1336 

17.0265 
19.8642 
22.7019 

9 

354-3300 

29.52750 

9.842500 

5-59233 

9 

2-43 

3-043 

9.5101 

23-7753 

25'5397 

SQUARE. 

WEIGHT. 

Square 

Square 

Square 

Milli- 

Kilo- 

Hecto- 

Kilo- 

centimetres 

metres  to 

metres  to 

Hectares 

grammes 

grammes 

gra 

mmes 

grammes 

to  square 

square 

square 

to  acres. 

to 

to 

to  c 

unces 

• 

o  pounds 

inches. 

feet. 

yards. 

grains. 

grains. 

avoirdupois. 

avoirdupois. 

I 

0.1550 

10.764 

1.196 

2.471 

I 

0.01543 

15432-36 

3-5274 

2.20462    ' 

2 

0.3100 

21.528 

2.392 

4.942 

2 

0.03086 

30864.71 

7.0548 

4.40924 

3 
4 

0.4650 
0.6200 

32.292 
43-055 

3.588 
4.784 

7-4I3 
9.884 

3 

4 

0.04630 
0.06173 

46297.07 
61729.43 

10 
14 

5822 
1096 

6.61  387 
8.81849 

5 

0.7750 

53-8I9 

5-980 

I2-355 

5 

0.07716 

77161.78 

17.6370 

11.02311 

6 
9 

0.9300 
1.0850 
1.2400 

I-395° 

64.583 
75-347 
86.1  1  1 
96.875 

7.176 
8.372 
9.568 
10.764 

14.826 
17.297 
19.768 
22.239 

6 

8 
9 

0.09259 
0.10803 
0.12346 
0.13889 

92594.14 
108026.49 
123458.85 
138891.21 

21.1644 
24.6918 
28.2192 
31.7466 

13.22773 
I5-43236 
17.63698 
19.84160 

CUBIC. 

WEIGHT. 

Cubic 
centimetres 
to  cubic 

Cubic 
decimetres 
to  cubic 

Cubic 
metres  to 
cubic 

Cubic 
metres  to 
cubic 

Quintals  to 
pounds  av. 

Milliers  or 
tonnes  to  pounds 

Kilogrammes 
to  ounces 

inches. 

inches. 

feet. 

yards. 

I 

0.06  10 

61.023 

35-3H 

1-308 

I 

220.46 

2204.6 

32.1507 

2 

0.1220 

122.047 

70.629 

2.616 

2 

440.92 

4409.2 

64.3015 

3 

0.1831 

183.070 

105.943 

3.924 

3 

661.39 

661- 

•9 

96.4522 

4 

0.2441 

244.094 

141.258 

5-232 

4 

881.85 

881* 

•5 

128.6030 

5 

0.3051 

3°5-II7 

176.572 

6.540 

5 

1102.31 

11023.1 

160.7537 

6 

0.3661 

366.140 

211.887 

7.848 

6 

1322.77 

13227.7 

192.9045 

7 

0.4272 

427.164 

247.201 

9.156 

7 

I543-24 

15432.4 

225.0552 

8 

0.4882 

488.187 

282.516 

10.464 

8 

1763.70 

17637.0 

2 

57.2059 

9 

0.5492 

549.210 

317.830 

11.771 

9 

1984.16 

19841 

.6 

2J 

59.3567 

By  the  concurrent  action  of  the  principal  governments  of  the  world  an  International  Bureau  of  Weights  and 
Measures  has  been  established  near  Paris.  Under  the  direction  of  the  International  Committee,  two  ingots  were 
cast  of  pure  platinum-iridium  in  the  proportion  of  9  parts  of  the  former  to  i  of  the  latter  metal.  From  one  of  these 
a  certain  number  of  kilogrammes  were  prepared,  from  the  other  a  definite  number  of  metre  bars.  These  standards 
of  weight  and  length  were  intercompared,  without  preference,  and  certain  ones  were  selected  as  Internationarproto- 
type  standards.  The  others  were  distributed  by  lot,  in  September,  1889,  to  tne  different  governments,  and  are  called 
National  prototype  standards.  Those  apportioned  to  the  United  States  were  received  in  1890,  and  are  kept  at  the 
Bureau  of  Standards  in  Washington,  D.  C. 

The  metric  system  was  legalized  in  the  United  States  in  1866. 

The  International  Standard  Metre  is  derived  from  the  Metre  des  Archives,  and  its  length  is  defined  by  the 
distance  between  two  lines  at  o°  Centigrade,  on  a  platinum-iridium  bar  deposited  at  the  International  Bureau  of 
Weights  and  Measures. 

The  International  Standard  Kilogramme  is  a  mass  of  platinum-iridium  deposited  at  the  same  place,  and  its  weight 
in  vacuo  is  the  same  as  that  of  the  Kilogramme  des  Archives. 

The  litre  is  equal  to  a  cubic  decimetre,  and  it  is  measured  by  the  quantity  of  distilled  water  which,  at  its  maxi- 
mum density,  will  counterpoise  the  standard  kilogramme  in  a  vacuum,  the  volume  of  such  a  quantity  of  water  being, 
as  nearly  as  has  been  ascertained,  equal  to  a  cubic  decimetre. 

SMITHSONIAN  TABLES. 


TABLE  3. 

EQUIVALENTS   OF   METRIC   AND   BRITISH    IMPERIAL   WEIGHTS 
AND   MEASURES.* 

(1)  METRIC  TO   IMPERIAL. 


LINEAR  MEASURE. 

MEASURE   OF   CAPACITY. 

zmim.ne.re  (mm.)     | 

=      0.03937    in. 

,  rnimmre  (ml.,  (.00,  |    =    ^ 

I  centimetre  (.01  m.) 
i  decimetre  (.1  m.) 

=           0.39370         " 
=            3-93701 
(39.370113      " 

i  centilitre  (.01  litre)        =  j  °*oi£24in" 
i  decilitre  (.1  litre)  .     .  =     0.176  pint. 

I  METRE  (m.)      .      .      . 

=  \      3.280843  ^ 

i  LITRE   (1,000  cub.  ) 

I  dekametre 

(    i.  09361  425  yds. 

centimetres  or  i    j-  =     1.75980  pints, 
cub.  decimetre)      ) 

(10  m.)       i  "     *     * 

—     J  O-936  1  4 

i  dekalitre  (10  litres)     .  =     2.200  gallons. 

I  hectometre 

i  hectolitre  (ioo  "   )    .  =     2.75  bushels. 

I09'36l42S 

i  kilolitre  (1,000  "  )     .  =    3.437  quarters. 

I  myriametre      ) 
(  1  0,000  m.)    j    *     ' 

=       6.21372  miles. 

APOTHECARIES'   MEASURE. 

=      o.ooi  mm. 

i    cubic    centi-  )       (   0.03520  fluid  ounce, 
metre      (i  >  =  }   0.28157  fluid  drachm, 
gramme  w't)  )       (  15.43236  grains  weight, 
i  cub.  millimetre  =      0.01693  minim. 

SQUARE  MEASURE. 

AVOIRDUPOIS   WEIGHT. 

I  sq.  centimetre      .     . 
I   sq.  decimetre          ) 
(ioo  sq.  centm.)     f 
I  sq.  metre  or  centi-  j 
are  (loosq.  dcm.)  j 
i  ARE  (ioo  sq.  m.) 
i  hectare  (ioo  ares 
or  10,000  sq.  m.) 

=       0.1550  sq.  in. 

_  i  10.7639  sq.  ft. 
(    1.1960  sq.  yds. 
=    119.60  sq.  yds. 

=       2.4711  acres. 

i  milligramme  (mgr.)  .    .  =   o.oi  543  grain, 
i  centigramme  (.01  gram.)  =    0.15432    " 
i  decigramme   (.1       "    )  =    1.54324  grains. 

i  dekagramme  (10  gram.)  =    5.64383  drams, 
i  hectogramme  (ioo  "    )  =    3.52739  oz. 
{2.2046223  Ibs. 
15432.3564 

grains. 

I  myriagramme  (iokilog.)=  22.04622  Ibs. 

i  quintal             (ioo     "    )=    1.96841  cwt. 

CUBIC   MEASURE. 

i  millier  or  tonne  |                     ~nQM~ 
(1,000  kilog.)    }     •    •-    0-9842  ton. 

I  cub.  centimetre 

(c.c.)  (1,000  cubic 

=    0.0610  cub.  in. 

TROY   WEIGHT. 

millimetres) 

I  cub.  decimetre 

(   0.03215  oz.  Troy. 

(c.d.)  (1,000  cubic 

=  61.024     "      " 

i  GRAMME  .     .  =  1   0.64301  pennyweight. 

centimetres) 

(  15.43236  grains. 

1  CorB"stefeTRE    I  . 

_  J  35-3  ^8  cub.  ft. 
i    i.  307954  cub.  yds. 

APOTHECARIES'  WEIGHT. 

(    0.25721  drachm. 

I  GRAMME      .    .    .    .  =  <    0.77162  scruple. 

(  1  5.43236  grains. 

NOTE. — The  METRE  is  the  length,  at  the  temperature  of  o°  C.,  of  the  platinum-iridium  bar  deposited  at  the 
International  Bureau  of  Weights  and  Measures  at  Sevres,  near  Paris,  France. 

The  present  legal  equivalent  of  the  metre  is  39.370113  inches,  as  above  stated. 

The  KILOGRAMME  is  the  mass  of  a  platinum-iridium  weight  deposited  at  the  same  place. 

The  LITRE  contains  one  kilogramme  weight  of  distilled  water  at  its  maximum  density  (4°  C.),  the  barometer  being 
at  760  millimetres. 

*In  accordance  with  the  schedule  adopted  under  the  Weights  and  Measures  (metric  system)  Act,  1897. 
SMITHSONIAN  TABLES. 


8  TABLES. 

EQUIVALENTS  OF   METRIC   AND   BRITISH   IMPERIAL  WEIGHTS 
AND   MEASURES. 

(2)  METRIC  TO  IMPERIAL 


LINEAR  MEASURE. 

MEASURE  OF  CAPACITY. 

2 

3 
4 

5 

Millimetres 
to 
inches. 

Metres 
to 
feet. 

Metres 
to 
yards. 

Kilo- 
metres to 
miles. 

Litres 
to 
pints. 

Dekalitres 
to 
gallons. 

Hectolitres 
to 
bushels. 

Kilolitres 
to 
quarters. 

0-039370II 
0.07874023 
0.11811034 
0.15748045 
0.19685056 

3.28084 
6.56169 
9.84253 
I3-I2337 
16.40421 

1.09361 

2.18723 
3.28084 
4-37446 
546807 

0.62137 
1.24274 
1.86412 
2.48549 
3.10686 

2 

3 

4 
5 

1.75980 
3.51961 
5.27941 
7.03921 
8.79902 

2.19975 

4-39951 
6.59926 
8.79902 
10.99877 

2.74969 
5-49938 
8.24908 
10.99877 
13.74846 

343712 
6.87423 
10.31135 
13.74846 
17.18558 

6 

I 

9 

0.23622068 
0.27559079 
0.31496090 
0.35433102 

19.68506 
22.96590 
26.24674 
29.52758 

6.56169 
7.65530 
8.74891 

9-84253 

3.72823 
4.34960 
4.97097 
5-59235 

6 

8 
9 

10.55882 
12.31862 
14.07842 
I5-83823 

13.19852 
15.39828 
17.59803 
19.79778 

16.49815 
19.24785 
21.99754 
2474723 

20.62269 
24.05981 
27.49692 
30.93404 

SQUARE  MEASURE. 

WEIGHT  (AVOIRDUPOIS). 

I 
2 

3 

4 
5 

Square 
centimetres 
to  square 
inches. 

Square 
metres  to 

IT 

Square 
metres  to 
square 
yards. 

Hectares 
to  acres. 

I 
2 

3 
4 
5 

Milli- 
grammes 
to 
grains. 

Kilogrammes 
to  grains. 

Kilo- 
grammes 
to 
pounds, 

Quintals 
to 
hundred- 
weights. 

0.15500 

0.31000 
0.46500 
0.62000 
0.77500 

10.76393 
21.52786 
32.29179 
43.05572 
53-8I965 

I.I9599 
2.39198 
3.58798 
4-78397 
5.97996 

2.4711 
4.9421 

74132 
9.8842 

12.3553 

0.01543 
0.03086 
0.04630 
0.06173 
0.07716 

15432.356 
30864.713 
46297.069 
61729.426 
77161.782 

2.20462 
4.40924 
6.61387 
8.81849 
II.023II 

1.96841 
3.93683 
5-90524 
7.87365 
9.84206 

6 

1 

9 

0.93000 
1.08500 
I-24OOO 
L3950I 

64.58357 
75-34750 
86.11143 
96.87536 

7-17595 
8.37194 

9.56794 
10.76393 

14.8263 
17.2974 
19.7685 
22.2395 

6 

I 

9 

0.09259 
0.10803 
0.12346 
0.13889 

92594.138 
108026.495 
123458.851 
138891.208 

13.22773 
1543236 
17.63698 
19.84160 

11.81048 
13.77889 

1574730 
17.71572 

CUBIC  MEASURE. 

APOTHE- 
CARIES' 
MEASURE. 

AVOIRDUPOIS 
(cont.) 

TROY  WEIGHT. 

APOTHE- 
CARIES' 
WEIGHT. 

Cubic 

decimetres 
to  cubic 
inches. 

Cubic 
metres  to 
cubic 
feet. 

Cubic 
metres  to 
cubic 
yards. 

Cub.  cen- 
timetres 
to  fluid 
drachms. 

Milliers  or 
tonnes  to 
tons. 

Grammes 
to  ounces 
Troy. 

,  Grammes 
to  penny- 
weights. 

Grammes 
to 
scruples. 

I 
2 

3 
4 

5 

61.02390 
122.04781 
183.07171 
244.09561 
305.H9S2 

35-3I476 
70.62952 
105.94428 
141.25904 
176.57379 

1.30795 
2.61591 
3.92386 
5.23182 

6-53977 

0.28157 
0.56314 
0.84471 
1.12627 
1.40784 

I 
2 

3 

4 
5 

0.98421 
1.96841 
2.95262 

3.93683 
4.92103 

0.03215 
0.06430 
0.09645 
0.12860 
0.16075 

0.64301 
1.28603 
1.92904 
2.57206 
3.21507 

0.77162 
1.54324 
2.31485 
3.08647 
3.85809 

6 

I 

9 

366.14342 
427.16732 
488.19123 
549-2I5I3 

211.88855 
247.20331 
282.51807 
317.83283 

7.84772 
9.15568 
10.46363 
11.77159 

1.68941 
1.97098 
2-25255 
2.53412 

6 

8 
9 

5-90524 
6.88944 

7.87365 
8.85786 

0.19290 
0.22506 
0.25721 
0.28936 

3.85809 
4.50110 
5.14412 
578713 

4.62971 
5.40132 
6.17294 
6.94456 

SMITHSONIAN  TABLES. 


TABLE  3. 

EQUIVALENTS  OF   BRITISH   IMPERIAL   AND   METRIC  WEIGHTS 
AND   MEASURES. 

(3)    IMPERIAL  TO   METRIC. 


LINEAR  MEASURE. 

MEASURE   OF  CAPACITY. 

f  25.400  milli- 

i  gill        .    .             .  —  1.42  decilitres. 

i  inch    =  \       metres, 
i  foot  (12  in.)     .    .=      0.30480   metre. 

i  pint  (4  gills)  .    .    .  =0.568  litre, 
i  quart  (2  pints)   .    .  =  1.136      litres. 

i  YARD  (3  ft.)     .    .  =      0.914399 
i  pole  (si  yd.)    .    .=      5.0292  metres. 

i  GALLON  (4  quarts)  =4.5459631  " 
i  peck  (2  galls.)    .     .  =  9.092 

i  chain  (22  yd.  or)   _              gg       „ 
100  links)         ) 
i  furlong  (220  yd.)  =  201.168         " 

i  bushel  (8  galls.)     .  =  3.637  dekalitres, 
i  quarter  (8  bushels)  =  2.909  hectolitres. 

AVOIRDUPOIS  WEIGHT. 

SQUARE  MEASURE. 

(64.8    milli- 

i  Grain  •                  •  —  < 

(6.4516  sq.  cen- 

i  square  inch          .    =   \     timetres. 

dram  —      T-772  grammes. 

f  9.2903  sq.  deci- 

ounce  (16  dr.)  .     .=    28.350         " 

i  sq.ft.  (144  sq.  in.)    =    )      metres, 
f  0.836126  sq. 
i  SQ.  YARD  (9  sq.  ft.)  =    \     metres. 

P°7"olo  grlins)°r  \  =      °-45359243  kilogr. 
stone  (14  lb.)  .    .=      6.350                " 

f  21?  201  sa  me- 

quarter  (28  lb.)     .=    12.70                  " 

i  rood  (40  perches)    =     10.117  ares. 

hundredweight  1     j  50.80                  " 
(ii2lb.)         J          I  0.5080  quintal. 

i  ACRE  (4840  sq.  yd.)  =      0.40468  hectare. 

{i.  0160  tonnes  or 

i  sq.  mile  (640  acres)  =  J259.oo  hectares. 

1016    kilo- 
grammes. 

TROY  WEIGHT. 

CUBIC  MEASURE. 

i  cub.  inch—    16.387  cub.  centimetres, 
i  cub.  foot  (1728  I        (0.028317  cub  me- 
cub.in.)     '       ]—  \     tre,    or   28.317 
I    cub.  decimetres. 

i  Troy  OUNCE  (480  )  s==3I.Io35  grammes, 
grains  avoir.)      ) 
i  pennyweight  (24  1   _  _                       ,« 
grains)                 f 

i  CUB.  YARD  (27  f  __  0.76455  cub.  metre. 

NOTE.  —  The  Troy  grain  is  of  the  same  weight  as 
the  Avoirdupois  grain. 

APOTHECARIES'  MEASURE. 

• 

APOTHECARIES'  WEIGHT. 

i  gallon  (8  pints  or  )           4-5459631  litres. 
1  60  fluid  ounces)  J 
I  fluid  ounce,  f  3  )           (28.4123  cubic 
(8  drachms)       f          }    centimetres. 
I  fluid  drachm,  f  3  I  __    f  3-55  1  5  cubic 
(60  minims)         f  ~=  \   centimetres, 
i  minim,  n\  (0.91146  )  (  0.05919  cubic 
grain  weight)       )      "   \   centimetres. 

i  ounce  (8  drachms)   =  31.1035  grammes, 
i  drachm,  31  (3  scru-  )  ggg           <« 
pies)                      f..  -••* 
i   scruple,   £i   (20  }                   g 
grains)                f 

NOTE.  —  The  Apothecaries'  ounce  is  of  the  same 
weight  as  the  Troy  ounce.      The  Apothecaries' 

NOTE.  —  The  Apothecaries'  gallon  is  of  the  same 

grain  is  also  of  the  same  weight  as  the  Avoir  dupois 

capacity  as  the  Imperial  gallon. 

grain. 

NOTE.  —The  YARD  is  the  length  at  62°  Fahr.,  marked  on  a  bronze  bar  deposited  with  the  Board  of  Trade. 

The  POUND  is  the  weight  of  a  piece  of  platinum  weighed  in  vacuo  at  the  temperature  of  o°  C.,  and  which  is  also 
deposited  with  the  Board  of  Trade. 

The  GALLON  contains  10  lb.  weight  of  distilled  water  at  the  temperature  of  62°  Fahr.,  the  barometer  being  at 
30  inches. 


SMITHSONIAN  TABLES. 


IO  TABLE  3. 

EQUIVALENTS  OF   BRITISH    IMPERIAL   AND   METRIC  WEIGHTS 
AND    MEASURES. 

(4)   IMPERIAL  TO  METRIC. 


LINEAR  MEASURE. 

MEASURE  OF  CAPACITY. 

Inches 
to 
centimetres. 

Feet 
to 
metres. 

Yards 
to 
metres. 

Miles 
to  kilo- 
metres. 

Quarts 
to 
litres. 

Gallons 
to 
litres. 

Bushels 
to 
dekalitres. 

Quarters 
to 
hectolitres. 

2-539998 
5.079996 
7.619993 
10.159991 
12.699989 

0.30480 
0.60960 
0.91440 
1.21920 
1.52400 

0.91440 
1.82880 
2.74320 
3.65760 
4.57200 

1.60934 
3.21869 
4.82803 

6-43737 
8.04671 

I 

2 

3 

4 
5 

1.13649 
2.27298 
340947 
4.54596 
5.68245 

4.54596 
9.09193 

I3-63789 
18.18385 
22.72982 

3-63677 
7-27354 
10.91031 
14.54708 
18.18385 

2.90942 
5.81883 
8.72825 
11.63767 
14.54708 

1  5-239987 
17.779984 
20.319982 
22.859980 

1.82880 
2.13360 
2.43840 
2.74320 

5.48640 
6.40080 

7.3I5I9 

8.22959 

9.65606 
11.26540 
12.87474 
14.48408 

6 
9 

6.81894 

7-95544 
9.09193 
10.22842 

27.27578 
31.82174 
36.36770 
40.91367 

21.82062 

25-45739 
29.09416 

32.73093 

17.45650 
20.36591 

23-27533 
26.18475 

SQUARE  MEASURE. 

WEIGHT  (AVOIRDUPOIS). 

Square 
inches 
to  square 
centimetres. 

Square 
feet 
to  square 
decimetres. 

Square 
yards  to 
square 
metres. 

Acres  to 
hectares. 

Grains 
to  milli- 
grammes. 

Ounces  to 
grammes. 

Pounds 
to  kilo- 
grammes. 

Hundred- 
weights to 
'quintals. 

I 

2 

3 

4 
5 

6.45*59 

12.90318 

19.35477 
25.80636 

32'25794 

9.29029 
18.58058 
27.87086 
37.16115 
46.45144 

0.83613 
1.67225 
2.50838 

3-3445° 

4.18063 

0.40468 
0.80937 
1.21405 
1.61874 
2.02342 

I 

2 

3 

4 

5 

64.79892 
129.59784 

I94-39675 
259-  i  9567 
323-99459 

28.34953 
56.69905 
85.04858 
113.39811 
141.74763 

0-45359 
0.90718 
1.36078 
1.81437 
2.26796 

0.50802 
1.01605 
1.52407 
2.03209 
2.54012 

6 
9 

38.70953 
45.16112 
51.61271 
58.06430 

55-74I73 
65.03201 
74.32230 
83.61259 

5.01676 

5.85288 
6.68901 
7.52513 

2.42811 
2.83279 
3.23748 
3.64216 

6 
9 

388.79351 
453-59243 
5*8.39135 
583.19026 

170.09716 
198.44669 
226.79621 
255.14574 

2.72155 

3.I75I5 
3.62874 
4.08233 

3.04814 
3-556l6 
4.06419 
4.57221 

CUBIC  MEASURE. 

APOTHE- 
CARIES' 
MEASURE. 

AVOIRDUPOIS 
(font.-). 

TROY  WEIGHT. 

APOTHE- 
CARIES' 
WEIGHT. 

Cubic 
inches 
to  cubic 
centimetres. 

Cubic  feet 
to 
cubic 
metres. 

Cubic 
yards 
to  cubic 
metres 

Fluid 
drachms 
to  cubic 
centi- 
metres. 

Tons  to 
milliers  or 
tonnes. 

Ounces  to 
grammes. 

Penny- 
weights to 
grammes. 

Scruples 
to 
grammes. 

I 

2 

3 
4 
5 

16.38702 
32.77404 
49.16106 
65.54808 
81.93511 

0.02832 
0.05663 
0.08495 
0.11327 
0.14158 

0.76455 
I.529II 
2.29366 
3.05821 
3.82276 

3-55I53 
7.10307 
10.65460 
14.20613 
17.75767 

2 

3 
4 
5 

1.01605 
2.03209 
3.04814 
4.06419 
5.08024 

31.10348 
62.20696 

93-3  *  044 
124.41392 

I55.5I740 

I.555I7 
3-II035 
4.66552 
6.22070 
7.77587 

1.29598 
2.59196 
3.88794 

5-l839i 
6.47989 

6 

i 

9 

98.32213 
114.70915 
131.09617 
147.48319 

0.16990 
0.19822 
0.22653 

0.25485 

4-58732 
5.35187 
6.11642 
6.88098 

21.30920 
24.86074 
28.41227 
31.96380 

6 

9 

6.09628 

7-iJ233 
8.12838 
9.14442 

186.62088 

217-72437 
248.82785 

279-93I33 

9.33104 
10.88622 
12.44139 
I3-99657 

7.77587 
9.07185 
10.36783 
11.66381 

SMITHSONIAN  TABLES. 


TABLE  4. 


II 


VOLUME  OF  A  CLASS  VESSEL  FROM  THE  WEIGHT  OF  ITS  EQUIVALENT 
VOLUME   OF    MERCURY   OR   WATER. 

If  a  glass  vessel  contains  at  f>  C,  P  grammes  of  mercury,  weighted  with  brass  weights  in  air  at 
760  mm.  pressure,  then  its  volume  in  c.  cm. 

at  the  same  temperature,  t,  \   V-=  PR   =  P^f 

at  another  temperature,  /i,  :   V  =  PR\  =  Ppjd  \  I  +  y  (t\  —  t)  \ 

p  =  the  weight,  reduced  to  vacuum,  of  the  mass  of  mercury  or  water  which,  weighed  with  brass 
weights,  equals  i  gramme  ; 

d '  =  the  density  of  mercury  or  water  at  /°C, 

and  7  =  o.ooo  025,  is  the  cubical  expansion  coefficient  of  glass. 


Temper- 
ature 
t 

WATER. 

MERCURY. 

R. 

Rlt  ti  —  10°. 

J?lf  /j  =  20°. 

R. 

Rit  /j  =  10°. 

/?!,  /!  =  20°. 

0° 

I.OOII92 

1.001443 

I.OOI693 

0.0735499 

0.0735683 

0.0735867 

I 

1133 

1358 

l6O9 

5633 

5798 

5982 

2 

IO92 

1292 

1542 

5766 

59H 

6898 

3 
4 
5 

1068 
I060 
1068 

1243 

I2IO 
"93 

H93 
I46O 

1443 

5900 

§ 

6029 
6144 
6259 

6213 
6328 
6443 

6 

I.OOI092 

I.OOII92 

I.OOI442 

0.0736301 

0.0736374 

0.0736558 

i 

II3I 
II84 

I2O6 
1234 

1456 

1485 

6434 
6568 

6490 
6605 

6674 

9 

I252 

1277 

1527 

6702 

6720 

6904 

10 

1333 

1333 

1584 

6835 

6835 

7020 

ii 

I.OOI428 

I.OOI4O3 

001653 

0.0736969 

0.0736951 

0.0737135 

12 

1536 

1486 

1736 

7103 

7066 

7250 

13 

1657 

1582 

I832 

7236 

7181 

7365 

14 

1790 

1690 

1940 

7370 

7297 

7481 

'5 

J935 

1810 

2O6O 

75°4 

7412 

750 

16 

1.002092 

1.001942 

I.002I93 

0.0737637 

0.0737527 

0.07377II 

17 

2261 

2086 

2337 

7771 

7642 

7826 

18 
19 

2441 
2633 

2241 
2407 

2491 
2658 

7905 
8039 

7757 
7872 

7941 
8057 

20 

2835 

2584 

2835 

8172 

7988 

21 

1.003048 

1.002772 

I.OO3O23 

0.0738306 

0.0738103 

0.0738288 

22 

3271 

2970 

3220 

8440 

8218 

8403 

23 

35°4 

3178 

3429 

8573 

8333 

8518 

24 

3748 

3396 

3647 

8707 

8449 

8633 

25 

4001 

3624 

3875 

8841 

8564 

8748 

26 

1.004264 

1.003862 

I.OO4II3 

0.0738974 

0.0738679 

0.0738864 

27 

4537 

4110 

4361 

9108 

8794 

8979 

28 

4818 

4366 

4616 

9242 

8910 

9094 

29 

5110 

4632 

4884 

9376 

9025 

9210 

30 

54io 

4908 

S1S9 

9510 

9140 

9325 

Taken  from  Landolt,  Bornstein,  and  Meyerhofifer's  Physikalisch-Chemische  Tabellen. 
SMITHSONIAN  TABLES. 


12 


TABLE  5. 
DIFFERENTIAL   COEFFICIENTS. 

INTEGRALS. 


DIFFERENTIAL 

COEFFICIENTS. 

INTEGRALS. 

T 

dx 

a* 
ex 

loge* 

sin.* 
cos.  x 
tan.  x 
cot.* 

sec.* 
cosec.  * 
sin.-1  * 
cos.—1  * 
tan.-1  * 
cot.-1  * 
sec.—1  * 
cosec.-1  * 
vers.-1  * 
covers.—1  x 

=nx»~l 

ax  loge  a 
e* 

i 
* 

COS.* 

—sin.  * 
sec.2  * 
—cosec.2  * 
sin.  * 

fx*dx 

faxdx 

fe*dx 
fdx 
J~x 

fcos.ax-dx 

/sin.  ax  •  dx 
/sec.2  ax  •  dx 

/cosec.2  ax  -  dx 
fs[n-  x  dx 

_*n+i 

W+I 

ax 

loge  <* 

ex 
loge* 
sin.  ax 

a 

—cos.  ax 

a 
tan.  ax 

cos.2  * 

COS.* 

~~  sin.2  * 

VC-*2) 

I 

a 
—cot.  ax 

a 
sec.  * 

—cosec.  * 

sin-^ 
a 

'   -cos-** 
a 

I  tan-1  2 
a           a 

i      ,    ,  * 

J   cos.2  * 
fCOS'  Xdx 

1   '  •     t     ax 
J   sm.2* 

r    dx 

JV(a2-*?) 

rdx 

Ja*+x* 

r    dx 

Vd-*") 
I 

I+*2 

I 

I+*2 

I 

*V/(*2-l) 

i 

cot.    * 
a            a 

(  i          ,  * 

*V(*2-i) 

I 

-  sec.    l  - 
a            a 

I   _,  _  __       !  * 

J  x\/(x2    a2) 

X/(2  *-*2) 

I 

r    dx 

cosec.    l  — 
a                a 

{vers.—1  * 
—covers.—1  * 

V/(2  OC-X>) 

J*S(2X-X*) 

Taylor's  series : 

u=f(x+h)=f(x)  +f'(x)h+f"(x)  ^  +/'"( 

The  remainder  after  the  first  w  terms  is  expressed  by 


•f0nfn+l(x+h-z)z*.dz. 


I.2.3 

Maclaurin's  series : 

u=f(x)=f(o)+f'(o)x+f"(o)  ~ 

^=3.14159265359 
i  =0.3 1 83098861 8 

^=9.86960440109 
^=2.71828182846 


=0.497  1  4987  269 


^=0.88622692546 


loge  10=2.30258509299 

log^(number)  =loge  (number)  •  logs  e 
_  logff(number) 
logeJ5 


SMITHSONIAN  TABLES. 


TABLE  6.  13 

VALUES  OF  RECIPROCALS,  SQUARES,  CUBES,  SQUARE  ROOTS,  OF 
NATURAL  NUMBERS. 


n 

.000.1 

n* 

A 

s 

n 

lOOO.Jl 

n> 

«* 

tf* 

10 

100.000 

100 

IOOO 

3.1623 

65 

15-3846 

4225 

274625 

8.0623 

ii 

90.9091 

121 

J331 

3.3166 

66 

15.1515 

4356 

287496 

8.1240 

12 

83-3333 

144 

1728 

3.4641 

67 

14.9254 

4489 

300763 

8.1854 

13 

76.9231 

I69 

2197 

3.6056 

68  • 

14.7059 

4624 

3  *  4432 

8.2462 

'4 

71.4286 

196 

2744 

3-7417 

69 

14.4928 

4761 

328509 

8,3066 

15 

66.6667 

225 

3375 

3-8730 

70 

14.2857 

4900 

343ooo 

8.3666 

16 

62.5000 

256 

4096 

4.0000 

71 

14.0845 

5041 

3579" 

8.4261 

17 

58.8235 

289 

4.1231 

72 

13.8889 

5^4 

373248 

8.4853 

18 

55-5556 

324 

§32 

4.2426 

73 

13.6986 

5329 

389017 

8.5440 

19 

52.6316 

361 

59 

4.3589 

74 

13-5135 

5476 

405224 

8.6023 

20 

50.0000 

400 

8000 

4.4721 

75 

I3-3333 

5625 

421875 

8.6603 

21 

47.6190 

441 

9261 

4.5826 

76 

I3-I579 

5776 

438976 

8.7178 

22 

45-4545 

484 

10648 

4.6904 

77 

12.9870 

5929 

456533 

8.7750 

23 

434783 

529 

12167 

4.7958 

78 

12.8205 

6084 

474552 

8.8318 

24 

41.6667 

576 

13824 

4.8990 

79 

12.6582 

6241 

493039 

8.8882 

25 

40.0000 

625 

15625 

5.0000 

80 

12.5000 

6400 

512000 

8.9443 

26 

27 

38.4615 
37-0370 

676 
729 

17576 
19683 

5.0990 
5.1962 

81 
82 

12.3457 
12.1951 

6561 
6724 

53  '44i 
551368 

9.0000 

9.0554 

28 
29 

35-7I43 
34.4828 

784 
84I 

21952 
24389 

5-2915 
5-3852 

83 
84 

1  2.0482 
11.9048 

6889 
7056 

571787 
592704 

9.1104 

9.1652 

30 

33-3333 

900 

27000 

5-4772 

85 

11.7647 

7225 

614125 

9.2195 

31 

32.2581 

961 

29791 

5-5678 

86 

11.6279 

7396 

636056 

9.2736 

32 

31.2500 

1024 

32768 

5-6569 

& 

11.4943 

7569 

658503 

9.3274 

33 

30-3030 

I089 

35937 

5-7446 

88 

11.3636 

7744 

681472 

9.3808 

34 

29.4118 

1156 

39304 

5-8310 

89 

11.2360 

7921 

704969 

9.4340 

35 

28.5714 

1225 

42875 

5.9161 

90 

n.  mi 

8100 

729000 

9.4868 

36 

27.7778 

1296 

46656 

6.0000 

91 

10.9890 

8281 

753571 

9-5394 

37 

27.0270 

1369 

50653 

6.0828 

92 

10.8696 

8464 

778688 

9-59I7 

38 
39 

26.3158 
25.6410 

1444 
1521 

54872 
59319 

6.1644 
6.2450 

93 
94 

10.7527 
10.6383 

8649 
8836 

8043^7 
830584 

9.6437 
9.6954 

40 

25.0000 
24.3902 

I6OO 

1681 

64000 
68921 

6.3246 
6.4031 

95 

96 

10.5263 
10.4167 

9025 
9216 

857375 
884736 

9.7468 
9.7980 

42 

23.8095 

1764 

74088 

6.4807 

97 

10.3093 

9409 

912673 

9.8489 

43 

23.2558 

1849 

79507 

6-5574 

98 

10.2041 

9604 

941192 

9.8995 

44 

22.7273 

1936 

85184 

6.6332 

99 

10.1010 

9801 

970299 

9.9499 

45 

22.2222 

2025 

91125 

6.7082 

100 

10.0000 

IOOOO 

IOOOOOO 

10.0000 

46 

47 

21.2766 

2116 
2209 

97336 
103823 

6.7823 
6-8557 

101 
IO2 

9.90099 
9.80392 

IO2OI 
10404 

1030301 

1061208 

10.0499 

10.0995 

48 
49 

20.8333 
20.4082 

2304 
2401 

110592 
117649 

6.9282 
7.0000 

103 
104 

9.70874 
9.61538 

10609 
I08I6 

1092727 
1124864 

10.1489 
10.1980 

50 

2O.OOOO 
19.6078 

2500 
2601 

125000 
132651 

7.0711 
7.1414 

105 

106 

9.52381 
9.43396 

II025 
11236 

1157625 

1191016 

10.2470 
10.2956 

52 
53 

19.2308 
18.8679 

2704 
2809 

140608 
148877 

7.2111 

7.2801 

107 
108 

9-34579 
9.25926 

II449 
11664 

1225043 
1259712 

10.3441 
10.3923 

54 

18.5185 

2916 

157464 

7.3485 

109 

9.I743I 

Il88l 

1295029 

10.4403 

55 

56 

18.1818 

17-8571 

3025 

166375 
175616 

7.4162 
7-4833 

110 

in 

9.09091 
9.00901 

1  2  100 
I232I 

1331000 
1367631 

10.4881 

10.5357 

57 

17-5439 

3249 

185193 

7-5498 

112 

8.92857 

12544 

1404928 

10.5830 

58 

17.2414 

3364 

195112 

7-6158 

"3 

8.84956 

12769 

1442897 

10.6301 

59 

16.9492 

348i 

205379 

7.6811 

114 

8.77193 

12096 

1481544 

10.6771 

60 

16.6667 

3600 

216000 

7.7460 

115 

8.69565 

13225 

1520875 

10.7238 

61 

16.3934 

3721 

226981 

7.8102 

116 

8.62069 

13456 

1560896 

10.7703 

62 

16.1290 

3844 

238328 

7.8740 

117 

8.54701 

13689 

1601613 

10.8167 

63 
64 

15-8730 
15.6250 

3969 
4096 

250047 
9  262144 

7.9373 
8.0000 

118 
119 

8.47458 
8.40336 

13924 
I4l6l 

1643032 
1685159 

10.8628 
10.9087 

SMITHSONIAN  TABLES. 


14  TABLE  6   (continued'}. 

VALUES  OF   RECIPROCALS,  SQUARES,  CUBES,  SQUARE   ROOTS, 
OF   NATURAL   NUMBERS. 


n 

1000.* 

* 

„• 

1* 

n 

1000.1 

* 

*• 

v* 

120 

8.33333 

14400 

1728000 

10.9545 

175 

5.71429 

30625 

5359375 

13.2288 

121 

8.26446 

14641 

I77I56I 

1  1  .0000 

176 

5.68182 

30976 

545r776 

13.2665 

122 
I23 

8.19672 
8.13008 

14884 
15129 

1815848 
1860867 

11.0454 
11.0905 

177 

178 

5.64972 
5.61798 

31329 
31684 

5545233 

13-3041 

U-34I7 

124 

8.06452 

15376 

1906624 

179 

5.58659 

32041 

5735339 

I3-379I 

125 

126 

:s 

8.00000 

7-93651 
7.87402 
7.81250 

15625 
15876 
16129 
16384 

I953I25 

2000376 
2048383 
2097IW 

11.1803 
11.2250 
11.2694 
H.3I37 

180 

181 
182 
183 

5-55556 
5.52486 

5-49451 
5.46448 

32400 
32761 
33I24 
33489 

5832000 

5929741 
6028568 
6128487 

13.4164 
U-4536 
13.4907 

!3-5277 

129 

7W94 

16641 

2146689 

n.3578 

184 

5-43478 

33856 

6229504 

13-5647 

130 

7.69231 

16900 

2197000 

11.4018 

185 

5-40541 

34225 

6331625 

13.6015 

I3I 

7.63359 

17161 

2248091 

11-4455 

186 

5-37634 

34596 

6434856 

13.6382 

132 
133 

7-57576 
7.51880 

17424 
17689 

2352637 

11.4891 
11.5326 

187 
188 

5-34759 

34969 
35344 

6539203 
6644672 

13-6748 
i3-7"3 

134 

7.46269 

17956 

2406104 

II.5758 

189 

5.29101 

35721 

6751269 

l3-7477 

135 

136 

137 
138 

7.40741 

7.35294 
7.29927 

7-24638 

18225 
18496 
18769 
19044 

2460375 
2515456 
2571353 
2628072 

11.6190 
11.6619 
11.7047 
n-7473 

190 

191 
192 

5.26316 

5.23560 
5-20833 
S-^^S 

36100 
36481 
36864 
37249 

6859000 
6967871 
7077888 
7189057 

13.7840 
13.8203 
13.8564 
13.8924 

139 

7.19424 

19321 

2685619 

11.7898 

194 

5.15464 

37636 

7301384 

13.9284 

140 

7.14286 

19600 

2744000 

11.8322 

195 

5.12821 

38025 

74M875 

13.9642 

141 

142 

7.09220 
7.04225 

19881 
20164 

2803221 
2863288 

11.8743 
11.9164 

196 
197 

5.10204 

5.07614 

38416 
38809 

7529536 
7645373 

14.0000 
1  4-03  57 

143 

6.99301 

20449 

2924207 

n-9583 

198 

5-05051 

39204 

7762392 

14.0712 

144 

6,94444 

20736 

2985984 

I2.OOOO 

199 

S-02S13 

39601 

7880599 

14.1067 

145 

6.89655 

21025 

3048625 

I2.O4I6 

200 

5.00000 

40000 

8000000 

14.1421 

146 

6.84932 

21316 

3II2I36 

12.0830 

201 

4.97512 

40401 

8120601 

14.1774 

148 

6.80272 
6.75676 

21609 
21904 

3176523 
3241792 

12.1244 
I2.I655 

2O2 
203 

4.95050 
4.92611 

40804 
41209 

8242408 
8365427 

14.2127 
14.2478 

149 

6.71141 

22201 

3307949 

12.2066 

2O4 

4.90196 

41616 

8489664 

14.2829 

150 

6.66667 

22500 

3375000 

12.2474 

205 

4-87805 

42025 

8615125 

14.3178 

151 

6.62252 

22501 

3442951 

12.2882 

206 

4-85437 

8741816 

I4-3527 

152 

6.57895 

23104 

3511808 

12.3288 

207 

4.83092 

42849 

8869743 

XQ«  ,• 
I4'3w5 

153 

6-53595 

23409 

3581577 

12.3693 

208 

4.80769 

43264 

8998912 

14.4222 

6.49351 

23716 

3652264 

12.4097 

209 

4-78469 

43681 

9129329 

14.4568 

155 

6.45161 

24025 

3723875 

12.4499 

210 

4.76190 

44100 

9261000 

14.4914 

156 

6.41026 

24336 

3796416 

12.4900 

211 

4-73934 

44521 

939393  i 

14.5258 

'57 

6.36943 

24649 

3869893 

12.5300 

212 

4.71698 

44944 

9528128 

14.5602 

158 
159 

6.32911 
6.28931 

24964 
25281 

3944312 
4019679 

12.5698 
12.6095 

2I3 

214 

4.69484 
4.67290 

45369 
45796 

9663597 
9800344 

14-5945 
14.6287 

160 

6.25000 

25600 

4096000 

12.6491 

215 

4.65116 

46225 

9938375 

14.6629 

161 

6.21118 

25921 

4173281 

12.6886 

216 

4.62963 

46656 

10077696 

14.6969 

162 

6.17284 

26244 

4251528 

12.7279 

217 

4.60829 

47089 

10218313 

14.7309 

163 

6.13497 

26569 

4330747 

12.7671 

218 

4.58716 

47524 

10360232 

14.7648 

164 

6.09756 

26896 

4410944 

12.8062 

219 

4.56621 

4796i 

10503459 

14.7986 

165 

6.06061 

27225 

4492125 

12.8452 

220 

4-54545 

48400 

10648000 

14.8324 

166 

6.02410 

27556 

4574296 

12.8841 

221 

4.52489 

48841 

10793861 

14.8661 

167 

5.98802 

27889 

4657463 

12.9228 

222 

4-50450 

49284 

10941048 

14.8997 

168 

5-95238 

28224 

4741632 

12.9615 

223 

4.48431 

49729 

11089567 

I4-9332 

169 

5.91716 

28561 

4826809 

13.0000 

224 

4.46429 

50176 

11239424 

14.9666 

170 

5.88235 

28900 

4913000 

13.0384 

225 

4.44444 

50625 

11390625 

15.0000 

171 
172 

5-84795 

29241 
29584 

5000211 
5088448 

13.0767 
13.1149 

226 
227 

4.42478 
440529 

51076 

11543176 
11697083 

1  5.0665 

173 
174 

5*78035 
5-747I3 

29929 
30276 

5268024 

13-1529 
13.1909 

228 
229 

$85 

5^4 
52441 

"852352 
12008989 

15.0997 
15-1327 

SMITHSONIAN  TABLES. 


TABLE  6  (continued).  l$ 

VALUES  OF  RECIPROCALS,  SQUARES,  CUBES,  AND  SQUARE  ROOTS,  OF 

NATURAL   NUMBERS. 


- 

IOOO.J 

, 

„« 

<• 

n 

1000.1 

* 

* 

V» 

230 

23I 

232 

4.34783 
4.32900 

4-3I034 

52900 
5336i 
53824 

12167000 
12326391 
12487168 

15.1658 
15-1987 
15-2315 

285 

286 
287 

3.50877 
3-49650 
3-48432 

81225 
81796 
82369 

23149125 
23393656 
23639903 

16.8819 
16.9115 
16.9411 

233 

4.29185 

54289 

12649337 

15.2643 

288 

3.47222 

82944 

23887872 

16.9706 

234 

4.27350 

54756 

12812904 

15.2971 

289 

3.46021 

83521 

24137569 

17.0000 

235 

4.25532 

55225 

12977875 

15-3297 

290 

3.44828 

84100 

24389000 

17.0294 

236 

4.23729 

55696 

13144256 

15.3623 

291 

3-43643 

84681 

24642171 

17.0587 

237 

4.21941 

56169 

13312053 

I5-3948 

292 

3.42466 

85264 

24897088 

17.0880 

238 

4.20168 

56644 

13481272 

15-4272 

293 

3.41297 

85849 

25153757 

17.1172 

239 

4.18410 

57121 

13651919 

154596 

294 

3.40136 

86436 

25412184 

17.1464 

240 

4.16667 

57600 

13824000 

15.4919 

295 

3-38983 

87025 

25672375 

17.1756 

241 

4.14938 

58081 

I399752I 

15.5242 

296 

3.37838 

87616 

25934336 

17.2047 

242 
244 

4.13223 
4-11523 
4-09836 

58564 
59049 
59536 

14172488 
14348907 
14526784 

1  5-  5  563 
15.5885 
15.6205 

297 
298 

299 

3.36700 
3-35570 
3-34448 

88209 
88804 
89401 

26198073 
26463592 
26730899 

17-2337 
17.2627 
17.2916 

245 

246 

4.08163 
4.06504 

60025 
60516 

14706125 
14886936 

15.6525 
15.6844 

300 

301 

3-33333 
3.32226 

90000 
90601 

27000000 
27270901 

17.3205 
17.3494 

247 

4.04858 

61009 

15069223 

15.7162 

302 

3.31126 

91204 

27543608 

17.3781 

248 
249 

4.03226 
4.01606 

61504 
62001 

15252992 
15438249 

15.7480 
I57797 

3°3 
304 

3-3J033 
3.28947 

91809 
92416 

27818127 
28094464 

17.4069 
J7-4356 

250 

251 

252 

4.00000 
3.98406 
3-96825 

62500 
63001 
63504 

15625000 

15813251 
16003008 

15.8114 
15.8430 
15-8745 

305 

306 

3°7 

3.27869 
3.26797 
3-25733 

93025 
93636 

28372625 
28652616 
28934443 

17.4642 
17.4929 
17.5214 

253 

3-95257 

64009 

16194277 

15.9060 

308 

3-24675 

94864 

29218112 

17.5499 

254 

3-93701 

64516 

16387064 

15-9374 

309 

3.23625 

95481 

29503629 

17.5784 

255 

3-92I57 

65025 

16581375 

15.9687 

310 

3.22581 

96100 

29791000 

17.6068 

256 

3.90625 

65536 

16777216 

16.0000 

3" 

3-21543 

96721 

30080231 

17.6352 

257 
258 

3.89105 
3-87597 

66049 
66564 

16974593 
I7I73512 

16.0312 
16.0624 

312 

3-20513 
3.19489 

97344 
97969 

30371328 
30664297 

17-6635 
17.6918 

259 

3.86100 

67081 

17373979 

16.0935 

3*4 

3.18471 

98596 

30959144 

17.7200 

260 

3-84615 

67600 

17576000 

16.1245 

315 

3.17460 

99225 

31255875 

17.7482 

261 
262 

3-83M2 
3.81679 

68121 
68644 

17779581 
17984728 

16.1555 
16.1864 

3i7 

3.16456 

3-  i  5457 

99856 
100489 

31554496 
3l855OI3 

17.7764 
17.8045 

263 
264 

3.80228 
3-78788 

69169 
69696 

18191447 
18399744 

16.2173 
16.2481 

319 

3-  i  4465 
3.13480 

101124 
101761 

32157432 
32461759 

17.8326 
17.8606 

265 

3.77358 

70225 

18609625 

16.2788 

320 

3.12500 

102400 

32768000 

17.8885 

266 

3-75940 

70756 

18821096 

16.3095 

321 

103041 

33076161 

17.9165 

267 

3.74532 

71289 

19034163 

16.3401 

322 

3-I0559 

103684 

33386248 

17.9444 

268 

3.73134 

71824 

19248832 

16.3707 

323 

3-09598 

104329 

33698267 

17.9722 

269 

37I747 

72361 

19465109 

16.4012 

324 

3.08042 

104976 

34012224 

18.0000 

270 

271 

272 

3-70370 
3.69004 
3.67647 

72900 
73441 
73984 

19683000 
19902511 
20123648 

16.4317 
16.4621 
16.4924 

325 

326 

3.07692 
3.06748 
3.05810 

106276 
106929 

34328125 
34645976 
34965783 

18.0278 
18.0355 
18.0831 

273 
274 

3.66300 
3.64964 

74529 
75076 

20346417 
20570824 

16.5227 
16.5529 

329 

3.04878 
3-0395  i 

107584 
108241 

35287552 
35611289 

18.1108 
18.1384 

275 

276 

3-63636 
3.62319 

76176 

20796875 
21024576 

16.5831 
16.6132 

330 

3.03030 
3-02115 

108900 
109561 

35937000 
36264691 

18.1659 
18.1934 

277 

3.61011 

76729 

21253933 

16.6433 

332 

3.01205 

110224 

36594368 

18.2209 

278 

3.59712 

77284 

21484952 

16.6733 

333 

3.00300 

110889 

36926037 

18.2483 

279 

3-58423 

77841 

21717639 

16.7033 

334 

2.99401 

111556 

37259704 

18.2757 

280 

281 

3.57U3 
3.55872 

78400 
78961 

21952000 
22188041 

16.7332 
16.7631 

335 

336 

2.98507 
2.97619 

112225 
112896 

37595375 
37933056 

18.3030 
18.3303 

282 
283 

3-53357 

79524 
80089 

22425768 
22665187 

16.7929 
16.8226 

337 
338 

2-96736 
2.958^8 

H3569 
114244 

38272753 
38614472 

18.3576 
18.3848 

284 

80656 

22906304 

16.8523 

339 

2.94985 

114921 

38958219 

18.4120 

SMITHSONIAN  TABLES. 


16 


TABLE  6 


VALUES  OF   RECIPROCALS,  SQUARES,  CUBES,  AND  SQUARE   ROOTS 
OF   NATURAL   NUMBERS. 


n 

lOOO.i 

* 

01 

v« 

w 

lOOO.i 

* 

* 

« 

340 

2.94118 

115600 

39304000 

18.4391 

395 

2.53165 

156025 

61629875 

19.8746 

341 

2.93255 

116281 

39651821 

18.4662 

396 

2.52525 

156816 

62099136 

19.8997 

342 

2.92398 

116964 

40001688 

18.4932 

2.51889 

157609 

62570773 

19.9249 

343 

2.91545 

117649 

40353607 

18.5203 

398 

2.51256 

158404 

63044792 

19.9499 

344 

2.90698 

118336 

40707584 

18.5472 

399 

2.50627 

159201 

63521199 

19.9750 

345 

2.89855 

119025 

41063625 

18.5742 

400 

2.50000 

160000 

64000000 

20.0000 

346 

2.89017 

119716 

41421736 

18.6011 

401 

2-49377 

160801 

64481201 

20.0250 

$ 

2.88184 

2.87356 

120409 
121104 

41781923 
42144192 

18.6279 
18.6548 

402 
403 

2.48756 
2.48139 

161604 
162409 

64964808 
65450827 

20.0499 
20.0749 

349 

2.86533 

121801 

42508549 

18.6815 

404 

2.47525 

163216 

65939264 

20.0998 

350 

2.85714 

122500 

42875000 

18.7083 

405 

2.46914 

164025 

66430125 

20.1246 

352 

2.84900 
2.84091 

123201 
123904 

43243551 
43614208 

18.7350 
18.7617 

406 
407 

2.46305 
2.45700 

164836 
165649 

66923416 
67419143 

20.1494 
20.1742 

353 

2.83286 

124609 

43986977 

18.7883 

408 

2.45098 

166464 

67917312 

20.1990 

354 

2.82486 

125316 

44361864 

18.8149 

409 

2-44499 

167281 

68417929 

20.2237 

355 

2.81690 

126025 

44738875 

18.8414 

410 

2.43902 

168100 

68921000 

20.2485 

356 

2.80899 

126736 

45118016 

18.8680 

411 

2.43309 

168921 

69426531 

20.2731 

357 

2.80112 

127449 

45499293 

18.8944 

412 

2.42718 

169744 

69934528 

20.2978 

358 

2.79330 

128164 

45882712 

18.9209 

413 

2.42131 

170569 

70444997 

20.3224 

359 

2.78552 

128881 

46268279 

18.9473 

414 

2.41546 

171396 

70957944 

20.3470 

360 

2.77778 

129600 

46656000 

18.9737 

415 

2.40964 

172225 

7M73375 

20.3715 

361 

2.77008 

130321 

47045881 

19.0000 

416 

2.40385 

173056 

71991296 

20.3961 

362 

2.76243 

131044 

47437928 

19.0263 

417 

2.39808 

173889 

72511713 

20.4206 

363 
364 

2.75482 
2.74725 

131769 
132496 

47832147 
48228544 

19.0526 
19.0788 

418 
419 

174724 

73034632 
73560059 

20.4450 
20.4695 

365 

2.73973 

133225 

48627125 

19.1050 

420 

2.38095 

176400 

74088000 

20.4939 

366 

2.73224 
2.72480 

133956 
134689 

49027896 
49430863 

19.1311 
19.1372 

421 
422 

2.37530 
2.36967 

177241 
178084 

74618461 
75I5I448 

20.5183 
20.5426 

368 

2.71739 

135424 

49836032 

«9-l833 

423 

2.36407 

178929 

75686967 

20.5670 

369' 

2.71003 

136161 

50243409 

19.2094 

424 

2-35849 

179776 

76225024 

20.5913 

370 

2.70270 

136900 

50653000 

19.2354 

425 

2.35294 

180625 

76765625 

20.6155 

371 

2.69542 

137641 

51064811 

19.2614 

426 

2-34742 

181476 

77308776 

20.6398 

372 

2.68817 

138384 

51478848 

19.2873 

427 

2.34192 

182329 

77854483 

20.6640 

373 

2.68097 

139129 

5l895II7 

19.3132 

428 

2-33645 

183184 

78402752 

20.6882 

374 

2.67380 

139876 

52313624 

429 

2.33100 

184041 

789535»9 

20.7123 

375 

2.66667 

140625 

52734375 

19.3649 

430 

2.32558 

184900 

79507000 

20.7364 

376 
377 

2.65957 
2.65252 

141376 

142129 

53157376 
53582633 

19.3907 
19.4165 

432 

2.32019 
2.31481 

185761 
186624 

80062991 
80621568 

20.7605 
20.7846 

378 
379 

2.64550 
2.63852 

142884 
143641 

54010152 
54439939 

19.4422 
19.4679 

433 
434 

2.30947 
2.30415 

187489 
188356 

81182737 
81746504 

20.8087 
20.8327 

380 

2.63158 
2.62467 

144400 
145161 

54872000 
55306341 

19.4936 
19.5192 

435 

436 

2.29885 
2.29358 

189225 
190096 

82312875 
82881856 

20.8567 
20.8806 

382 
383 

2.61780 

2.61097 

145924 
146689 

55742968 
56181887 

19.5448 
19.5704 

438 

2.28833 
2.28311 

190969 
191844 

83453453 
84027672 

20.9045 
20.9284 

384 

2.60417 

147456 

56623104 

19-5959 

439 

2.27790 

192721 

84604519 

20.9523 

385 

2.59740 

148225 

57066625 

19.6214 

440 

2.27273 

193600 

85184000 

20.9762 

386 

148996 

57512456 

19.6469 

441 

2.26757 

194481 

85766121 

2I.OOOO 

387 

2.58398 

149769 

57960603 

19.6723 

442 

2.26244 

195364 

86350888 

21.0238 

388 

2.57732 

150544 

58411072 

19.6977 

443 

2.25734 

196249 

86938307 

21.0476 

389 

2.57069 

151321 

58863869 

19.7231 

444 

2.25225 

197136 

87528384 

21.0713 

390 

2.56410 

152100 

59319000 

19.7484 

445 

2.24719 

198025 

88121125 

21.0950 

392 

2.55754 
2.55102 

152881 
153664 

59776471 
60236288 

19.7737 
19.7990 

446 

447 

2.24215 
2.23714 

198916 
199809 

88716536 
89314623 

2I.II87 
21.1424 

393 

2.54453 

154449 

60698457 

19.8242 

448 

2.23214 

200704 

89915392 

21.  1660 

394 

2.53807 

155236 

e.^ 

19.8494 

449 

2.22717 

201601 

90518849 

21.1896 

SMITHSONIAN  TABLES. 


TABLE  6  (continued).  1 7 

VALUES   OF   RECIPROCALS,   SQUARES,   CUBES,   AND   SQUARE    ROOTS 
OF    NATURAL    NUMBERS. 


n 

,000.1 

» 

* 

i* 

n 

IOOO.J 

- 

if 

i* 

450 

2.22222 

2O25OO 

9II25OOO 

21.2132 

505 

1.98020 

255025 

128787625 

22.4722 

451 

2.21730 

2O34OI 

9I73385I 

21.2368 

506 

1.97628 

256036 

129554216 

22.4944 

452 

2.21239 

204304 

92345408 

21.2603 

5°7 

1.97239 

257049 

130323843 

22.5167 

453 
454 

2.20751 
2.2O264 

205209 
2o6ll6 

92959677 
93576664 

21.2838 
21.3073 

508 
509 

1.96850 

1.96464 

258064 
259081 

131096512 
131872229 

22.5389 
22.5610 

455 

456 

2.19780 
2.19298 

207025 
207936 

94818816 

21.3307 
21.3542 

510 

511 

1.96078 
1  -95695 

260100 
261121 

132651000 
1  3343283  i 

22.5832 
22.6053 

457 

2.l88l8 

208849 

95443993 

21.3776 

512 

r-95312 

262144 

134217728 

22.6274 

458 
459 

2.18341 
2.17865 

209764 
2I068I 

96071912 
96702579 

21.4009 
21.4243 

1.94932 
1-94553 

263169 
264196 

135005697 
135796744 

22.6495 
22.6716 

460 

2.I739I 

2II6OO 

97336000 

21.4476 

515 

I-94I75 

265225 

136590875 

22.6936 

461 

2.16920 

2I252I 

97972181 

21.4709 

516 

1.93798 

266256 

137388096 

22.7156 

462 

2.16450 

213444 

98611128 

21.4942 

5*7 

1.93424 

267289 

138188413 

22.7376 

463 

2.15983 

214369 

99252847 

21.5174 

518 

1.93050 

268324 

1  38991  832 

22.7596 

464 

215296 

99897344 

21.5407 

5*9 

1.92678 

269361 

^9798359 

22.7816 

465 

2.15054 

216225 

100544625 

21.5639 

520 

1.92308 

270400 

140608000 

22.8035 

466 

2.14592 

217156 

101194696 

21.5870 

521 

1.91939 

271441 

141420761 

22.8254 

467 

2.I4I33 

218089 

101847563 

21.6102 

522 

272484 

142236648 

22.8473 

468 
469 

2.13675 
2.13220 

219024 
219961 

102503232 
103161709 

21.6333 
21.6564 

523 
524 

1.91205 
1.90840 

273529 
274576 

143055667 
143877824 

22.8692 
22.8910 

470 

2.12766 

22O9OO 

103823000 

21.6795 

525 

1.90476 

275625 

144703125 

22.9129 

471 

2.12314 

221841 

104487111 

21.7025 

526 

1.90114 

276676 

I4553I576 

22.9347 

472 

2.II864 

222784 

105154048 

21.7256 

527 

1  -897  53 

277729 

146363183 

22.9565 

473 

2.II4I6 

223729 

105823817 

21.7486 

528 

1.89394 

278784 

147197952 

22.9783 

474 

2.IO97O 

224676 

106496424 

21.7715 

529 

1.89036 

279841 

148035889 

23.0000 

475 

2.10526 

225625 

107171875 

21.7945 

530 

1.88679 

280900 

148877000 

23.0217 

476 

2.IOO84 

226576 

107850176 

21.8174 

531 

1.88324 

281961 

149721291 

23-0434 

477 

2.09644 

227529 

108531333 

21.8403 

532 

1.87970 

283024 

150568768 

23.0651  ; 

478 

2.09205 

228484 

109215352 

21.8632 

533 

1.87617 

284089 

I5HI9437 

23.0868 

479 

2.08768 

229441 

109902239 

21.8861 

534 

1.87266 

285156 

152273304 

23.1084 

480 

2-08333 

230400 

110592000 

21.9089 

535 

1.86916 

286225 

I53I30375 

23.1301 

481 

2.0790C 

231361 

111284641 

21.9317 

536 

1.86567 

287296 

153990656 

482 
483 

2.07469 
2.07039 

232324 
233289 

111980168 
112678587 

21-9545 
21.9773 

537 

538 

1.86220 
1.85874 

288369 
289444 

154854153 
155720872 

23-1733 
23.1948 

484 

2.06612 

234256 

"3379904 

22.0000 

539 

1.85529 

290521 

156590819 

23.2164 

485 

486 

2.06186 
2.05761 

235225 
236196 

114084125 
114791256 

22.0227 

22.0454 

540 

54i 

1.85185 
1.84843 

291600 
292681 

157464000 
158340421 

23-2379 
23.2594 

487 

2-05339 

237169 

115501303 

22.O68I 

542 

1.84502 

293764 

159220088 

23.2809 

488 

2.04918 

238144 

116214272 

22.0907 

543 

1.84162 

294849 

160103007 

23.3024 

489 

2.04499 

239I2I 

116930169 

22.1133 

544 

1.83824 

295936 

160989184 

23-3238 

490 

2.O4O82 

24OIOO 

117649000 

22.1359 

545 

1.83486 

297025 

161878625 

23-3452 

491 

2.03666 

241081 

118370771 

22.1585 

546 

1.83150 

298116 

162771336 

23.3666 

492 

2.03252 

242064 

119095488 

22.I8II 

547 

1.82815 

299209 

163667323 

23.3880 

493 

2.02840 

243049 

119823157 

22.2036 

548 

1.82482 

300304 

164566592 

23.4094 

494 

2.02429 

244036 

120553784 

22.2261 

549 

1.82149 

301401 

165469149 

23-4307 

495 

2.O2O2O 

245025 

121287375 

22.2486 

550 

1.81818 

302500 

166375000 

23.4521 

496 

2.0l6l3 

246016 

122023936 

22.2711 

551 

1.81488 

303601 

167284151 

23-4734 

497 

2.OI2O7 

247009 

122763473 

22.2935 

552 

1.81159 

304704 

168196608 

23-4947 

498 
499 

2.00803 
2.00401 

248004 
249OOI 

123505992 
124251499 

22.3159 
22.3383 

553 
554 

1.80832 
1.80505 

$&$ 

169112377 
170031464 

23.5160 
23-5372 

500 

2.00000 
I.9900I 

250000 
25IOOI 

125000000 
125751501 

22.3607 
22.3830 

555 

556 

.80180 
.79856 

308025 
309136 

170953875 
171879616 

23.5584 
23.5797 

502 

1.99203 

252004 

i  26506008 

22.4054 

557 

•79533 

310249 

172808693 

23.6008 

5°3 

1.98807 

253009 

127263527 

22.4277 

558 

.79211 

311364 

173741112 

23.6220 

5°4 

1.98413 

254016 

128024064 

22.4499 

559 

.78891 

312481 

174676879 

23.6432 

SMITHSONIAN  TABLES. 


1 8  TABLE  6   (continued). 

VALUES  OF   RECIPROCALS,  SQUARES,  CUBES,  AND  SQUARE    ROOTS 
OF    NATURAL    NUMBERS. 


n 

lOOO.i 

tfi 

«8 

V* 

n 

IOOO.I 

n* 

«3 

V* 

560 

J-7857i 

313600 

175616000 

23.6643 

615 

1.62602 

378225 

232608375 

24.7992 

56i 
562 

563 

1-78253 
1.77936 
1.77620 

314721 

176558481 
177504328 
178453547 

23.6854 
23.7065 
23.7276 

616 
617 
618 

1.62338 

1.62075 
1.61812 

380689 
381924 

233744896 
234885113 
236029032 

24.8193 

24-8395 
24.8596 

/- 

564 

I-77305 

318096 

179406144 

23.7487 

619 

1.61551 

383161 

237176659 

24.8797 

565 

1.76991 

319225 

180362125 

23.7697 

620 

1.61290 

384400 

238328000 

24.8998 

566 

1.76678 

320356 

181321496 

23.7908 

621 

1.61031 

385641 

239483061 

24.9199 

567 

1.76367 

321489 

182284263 

23.8118 

622 

1.60772 

386884 

240641848 

24-9399 

568 

-*•**  >- 

1.76056 

322624 

183250432 

23.8328 

623 

1.60514 

388129 

241804367 

24.9600 

569 

1-75747 

323761 

184220009 

23-8537 

624 

1.60256 

389376 

242970624 

24.9800 

570 

1  -7  5439 

324900 

185193000 

23.8747 

625 

1.60000 

390625 

244140625 

25.0000 

57i 

I-75I3I 

326041 

186169411 

23.8956 

626 

1-59744 

391876 

2453  !  4376 

25.0200 

572 

1.74825 

327184 

187149248 

23.9165 

627 

1.59490 

393  i  29 

246491883 

25.0400 

573 

1.74520 

328329 

188132517 

23-9374 

628 

1.59236 

394384 

247673132 

25.0599 

574 

1.74216 

329476 

189119224 

23-9583 

629 

1.58983 

395641 

248858189 

25.0799  1 

575 

i-739I3 

330625 

190109375 

23.9792 

630 

1-58730 

396900 

25OO47OOO 

25.0998 

576 

1.73611 

33^76 

191102976 

24.0000 

631 

1.58479 

398161 

25I23959! 

25.1197 

577 

1.73310 

332929 

192100033 

24.0208 

632 

1.58228 

399424 

252435968 

25.1396 

578 

1.73010 

334084 

193100552 

24.0416 

633 

1.57978 

400689 

253636137 

25-1595 

579 

1.72712 

335241 

194104539 

24.0624 

634 

1.57729 

401956 

254840104 

25.1794 

580 

1.72414 

336400 

195112000 

24.0832 

635 

1.57480 

403225 

256047875 

25.1992 

581 

1.72117 

33756i 

196122941 

24.1039 

636 

1-57233 

404496 

257259456 

25.2190 

582 

1.71821 

338724 

I97I37368 

24.1247 

637 

1.56986 

405769 

258474853 

25.2389 

583 

1.71527 

339889 

198155287 

24.1454 

638 

1.56740 

407044 

259694072 

25.2587 

584 

1-71233 

341056 

199176704 

24.1661 

639 

1.56495 

408321 

260917119 

25.2784 

585 

1.70940 

342225 

200201625 

24.1868 

640 

1.56250 

409600 

262144000 

25.2982 

586 

1.70648 

343396 

201230056 

24.2074 

641 

1.56006 

410881 

263374721 

25.3180 

587 

1-70358 

344569 

202262003 

24.2281 

642 

I-55763 

412164 

264609288 

25-3377 

588 

1.70068 

345744 

203297472 

24.2487 

643 

L55521 

413449 

265847707 

25-3574 

589 

1.69779 

346921 

204336469 

24-2693 

644 

1.55280 

4H736 

267089984 

25-3772 

590 

1.69492 

348100 

205379000 

24.2899 

645 

L55039 

416025 

268336125 

25-3969 

591 

1.69205 

349281 

206425071 

24.3105 

646 

1-54799 

4173*6 

269586136 

25.4165 

592 

1.68919 

350464 

207474688 

24.3311 

647 

1.54560 

418609 

270840023 

25.4362 

593 

1.68634 

35  l  649 

208527857 

24.3516 

648 

I-5432I 

419904 

272097792 

25-4558 

594 

1.68350 

352836 

209584584 

24.3721 

649 

1.54083 

421201 

273359449 

25.4755 

595 

1.68067 

354025 

210644875 

24.3926 

650 

1.53846 

422500 

274625000 

25.4951 

596 

1.67785 

3552i6 

211708736 

24.4131 

651 

1.53610 

423801 

275894451 

25-5M7 

597 

1.67504 

356409 

212776173 

24-4336 

652 

1-53374 

425104 

277167808 

25-5343 

i98 

1.67224 

357604 

213847192 

24.4540 

653 

I-53I39 

426409 

278445077 

25-5539 

599 

1.66945 

3588oi 

214921799 

24.4745 

654 

1.52905 

427716 

279726264 

25.5734 

600 

1.66667 

360000 

216000000 

24.4949 

655 

1.52672 

429025 

281011375 

25-5930 

601 

1.66389 

361201 

217081801 

24-5r53 

656 

i.52439 

430336 

282300416 

25.6125 

602 

1.66113 

362404 

218167208 

24-5357 

657 

1.52207 

431649 

283593393 

25.6320 

603 

1.65837 

363609 

219256227 

24.5561 

658 

1.51976 

432964 

284890312 

25-651.5 

604 

1-65563 

364816 

220348864 

24.5764 

659 

i.5'745 

43428i 

286191179 

25.6710 

605 

1.65289 

366025 

221445125 

24.5967 

660 

I-SISIS 

435600 

287496000 

25.6905 

606 

1.65017 

367236 

222545016 

24.6171 

661 

1.51286 

436921 

288804781 

25.7099 

607 

1.64745 

368449 

223648543 

24.6374 

662 

1.51057 

438244 

290117528 

25-7294 

608 

1.64474 

369664 

224755712 

24.6577 

663 

1.50830 

439569 

291434247 

25.7488 

609 

1.64204 

37o88i 

225866529 

24.6779 

664 

1.50602 

440896 

292754944 

25.7682  ; 

610 

1-63934 

372100 

226981000 

24.6982 

665 

i.50376 

442225 

294079625 

25.7876 

611 

1.63666 

373321 

228099131 

24.7184 

666 

1.50150 

443556 

295408296 

25.8070 

612 

1  -63399 

374544 

229220928 

24-7386 

667 

1.49925 

444889 

296740963 

25.8263 

613 

1.63132 

375769 

230346397 

24.7588 

668 

1.49701 

446224 

298077632 

25-8457 

614 

1.62866 

376996 

23H75544 

24.7790 

669 

1.49477 

44756i 

299418309 

25.8650 

SMITHSONIAN  TABLES. 


TABLE  6  (continued). '  19 

VALUES   OF   RECIPROCALS,  SQUARES,  CUBES,  AND  SQUARE   ROOTS 
OF   NATURAL   NUMBERS. 


n 

iooo.i 

n* 

„. 

i* 

n 

iooo.i 

* 

., 

v* 

670 

1.49254 

448900 

300763000 

25.8844 

725 

I-3793I 

525625 

381078125 

26.9258 

671 

1.49031 

450241 

302111711 

25.9037 

726 

I-3774I 

527076 

382657176 

26.9444 

672 

1.48810 

45*584 

303464448 

25.9230 

727 

I-37552 

528529 

384240583 

26.9629 

673 

1.48588 

452929 

304821217 

25.9422 

728 

1-37363 

529984 

385828352 

26.9815 

674 

1.48368 

454276 

306182024 

25.9615 

729 

I.37I74 

53I44I 

387420489 

27.0000 

675 

1.48148 

455625 

307546875 

25.9808 

730 

1.36986 

532900 

389017000 

27.0185 

676 

1.47929 

456976 

308915776 

26.0000 

731 

1-36799 

390617891 

27.0370 

677 

1.47710 

310288733 

26.0192 

732 

1.36612 

535824 

392223168 

27.0555 

678 
679 

1.47493 
1.47275 

459684 
461041 

311665752 
313046839 

26.0384 
26.0576 

733 

734 

1.36426 
1.36240 

537289 
538756 

393832837 
395446904 

27.0740 
27.0924 

680 

1.47059 

462400 

314432000 

26.0768 

735 

1.36054 

540225 

397065375 

27.1109 

68  1 

1.46843 

463761 

315821241 

26.0960 

736 

1-35870 

541696 

398688256 

27.1293 

682 

1.46628 

465124 

317214568 

26.1151 

737 

1.35685 

543169 

400315553 

27.1477 

683 

1.46413 

466489 

318611987 

26.1343 

738 

1.35501 

544644 

401947272 

27.1662 

684 

1.46199 

467856 

320013504 

26.1534 

739 

I-353l8 

546121 

403583419 

27.1846 

685 

1  4598  5 

469225 

321419125 

26.1725 

740 

1.35135 

5476oo 

405224000 

27.2029 

686 

1-45773 

470596 

322828856 

26.1916 

741 

1-34953 

549081 

406869021 

27.2213 

687 

1.45560 

471969 

324242703 

26.2107 

742 

i-3477i 

550564 

408518488 

27.2397 

688 

145349 

473344 

325660672 

26.2298 

743 

1-3459° 

552049 

410172407 

27.2580 

689 

145*38 

474721 

327082769 

26.2488 

744 

1.34409 

553536 

411830784 

27.2764 

690 

1.44928 

476100 

328509000 

26.2679 

745 

1.34228 

555025 

413493625 

27.2947 

691 

1.44718 

477481 

329939371 

26.2869 

746 

1.34048 

556516 

415160936 

27.3130 

692 
693 

1.44509 
1.44300 

478864 
480249 

331373888 
332812557 

26.3059 
26.3249 

747 
748 

1.33869 
1.33690 

558009 
559504 

416832723 
418508992 

27.3313 
27.3496 

694 

1.44092 

481636 

334255384 

26.3439 

749 

1-335" 

561001 

420189749 

27.3679 

695 

1.43885 

483025 

335702375 

26.3629 

750 

1-33333 

562500 

421875000 

27.3861 

696 

1.43678 

484416 

337153536 

26.3818 

751 

I-33I56 

564001 

423564751 

27.4044 

697 

1.43472 

485809 

338608873 

26.4008 

752 

1.32979 

565504 

425259008 

27.4226 

698 

1.43266 

487204 

340368392 

26.4197 

753 

1.32802 

567009 

426957777 

27.4408 

699 

1.43062 

488601 

341532099 

26.4386 

754 

1.32626 

568516 

428661064 

27.4591 

700 

1.42857 

490000 

343000000 

26.4575 

755 

1.32450 

570025 

430368875 

274773 

701 

1.42653 

491401 

344472101 

26.4764 

756 

1.32275 

571536 

432081216 

27-4955 

702 

1.42450 

492804 

345948408 

26.4953 

757 

1.32100 

573049 

433798093 

27-5136 

703 
704 

1.42248 
1.42045 

494209 
495616 

347428927 
348913664 

26.5141 
26.5330 

758 
759 

1.31926 
1.31752 

574564 
576081 

4355I9512 
437245479 

27-5318 
27.5500 

705 

1.41844 

497025 

350402625 

26.5518 

760 

i-3I579 

577600 

438976000 

27.568! 

706 

1.41643 

498436 

351895816 

26.5707 

761 

1.31406 

579121 

440711081 

27.5862 

707 

1.41443 

499849 

353393243 

26.5895 

762 

i.3I234 

580644 

442450728 

27-6043 

708 

1.41243 

501264 

354894912 

26.6083 

763 

1.31062 

582169 

444194947 

27.6225 

709 

1.41044 

502681 

356400829 

26.6271 

764 

1.30890 

583696 

445943744 

27.6405 

710 

1.40845 

504100 

357911000 

26.6458 

765 

1.30719 

585225 

447697125 

27.6586 

711 

712 

1.40647 
1.40449 

505521 
506944 

359425431 
360944128 

26.6646 
26.6833 

766 

767 

1.30548 
1.30378 

586756 
588289 

449455096 
451217663 

27.6767 
27.6948 

713 

1.40252 

508369 

362467097 

26.7021 

768 

1.30208 

589824 

452984832 

27.7128 

1.40056 

509796 

363994344 

26.7208 

769 

1.30039 

59i36i 

454756609 

27.7308 

715 

1.39860 

5II225 

365525875 

26.7395 

770 

1.29870 

592900 

456533000 

27.7489 

716 

1.39665 

512656 

367061696 

26.7582 

771 

1.29702 

594441 

458314011 

27.7669 

717 

1.39470 

*JS^I 

514089 

368601813 

26.7769 

772 

1.29534 

595984 

460099648 

27.7849 

718 

1.39276 

5T5524 

370146232 

26.7955 

773 

1.29366 

597529 

461889917 

27.8029 

719 

1.39082 

516961 

371694959 

26.8142 

774 

1.29199 

599076 

463684824 

27.8209 

720 

721 

722 

1.38889 
.1.38696 

"1.38504 

518400 
519841 
521284 

373248000 
374805361 
376367048 

26.8328 
26.8514 
26.8701 

775 

776 
777 

1.28700 

600625 
602176 
603729 

465484375 
467288576 

469097433 

27.8388 
27.8568 
27.8747 

723 
724 

1.38313 

1.38122 

522729 
524176 

377933067 
379503424 

26.8887 
26.9072 

778 
779 

1-28535 
1.28370 

605284 
606841 

470910952 
472729139 

27.8927 

27.9106 

SMITHSONIAN  TABLES. 


2O  TABLE  6  (continued}. 

VALUES  OF   RECIPROCALS,   SQUARES,   CUBES,   AND   SQUARE   ROOTS 
OF   NATURAL   NUMBERS. 


n 

iooo4 

H* 

«3 

jf* 

n 

iooo.i 

«2 

«8 

fW 

780 

1.28205 

608400 

474552000 

27.9285 

835 

1.19760 

697225 

582182875 

28.8964 

781 

1.28041 

609961 

476379541 

27.9464 

836 

1.19617 

698896 

584277056 

28.9137 

782 

1.27877 

611524 

478211768 

27.9643 

837 

1.19474 

700569 

586376253 

28.9310 

783 

1.27714 

613089 

480048687 

27.9821 

838 

1.19332 

702244 

588480472 

28.9482 

784 

1.27551 

614656 

481890304 

28.0000 

839 

1.19190 

703921 

590589719 

28.9655 

785 

1.27389 

6l6225 

483736625 

28.0179 

840 

1.19048 

705600 

592704000 

28.9828 

786 

1.27226 

617796 

485587656 

28.0357 

841 

1.18906 

707281 

594823321 

29.0000 

787 

1.27065 

619369 

487443403 

28.0535 

842 

1.18765 

708964 

596947688 

29.0172 

788 
789 

1.26904 
1.26743 

620944 
622521 

489303872 
491169069 

28.0713 
28.0891 

843 
844 

1.18624 
1.18483 

710649 
712336 

599077107 
601211584 

29-0345 
29.0517 

790 

1.26582 

624IOO 

493039000 

28.1069 

845 

1.18343 

714025 

603351125 

29.0689 

791 

1.26422 

625681 

494913671 

28.1247 

846 

1.18203 

715716 

605495736 

29.0861 

792 

1.26263 

627264 

496793088 

28.1425 

847 

1.18064 

717409 

607645423 

29.1033 

793 

1.26103 

628849 

498677257 

28.1603 

848 

1.17925 

719104 

609800192 

29.1204 

794 

1.25945 

630436 

500566184 

28.1780 

849 

1.17786 

720801 

611960049 

29.1376 

795 

1.25786 

632025 

502459875 

28.1957 

850 

1.17647 

722500 

614125000 

29.1548 

796 

1.25628 

633616 

504358336 

28.2135 

851 

1.17509 

724201 

616295051 

29.1719 

798 

1.25471 
1.25313 

635209 
636804 

506261573 
508169592 

28.2312 
28.2489 

852 
853 

1.17371 
1.17233 

725904 
727609 

618470208 
620650477 

29.1890 
29.2062 

799 

1.25156 

638401 

510082399 

28.2666 

854 

1.17096 

729316 

622835864 

29.2233 

800 

1.25000 

64OOOO 

512000000 

28.2843 

855 

1.16959 

731025 

625026375 

29.2404 

801 

1.24844 

641601 

5I392240I 

28.3019 

856 

1.16822 

732736 

627222016 

29-2575 

802 

1.24688 

643204 

515849608 

28.3196 

857 

1.16686 

734449 

629422793 

29.2746 

803 

I-24533 

644809 

517781627 

28.3373 

858 

1.16550 

736164 

631628712 

29.2916 

804 

1.24378 

646416 

519718464 

28.3549 

859 

1.16414 

73788i 

633839779 

29.3087 

805 

806 

1.24224 
1.24069 

648025 
649636 

52I660I25 
523606616 

28.3725 
28.3901 

860 

86  1 

1.16279 

1.16144 

7396oo 
741321 

636056000 
638277381 

29.3258 
29.3428 

807 

1.23916 

651249 

525557943 

28.4077 

862 

1.16009 

743044 

640503928 

29.3598 

808 

1.23762 

652864 

527514112 

28.4253 

863 

1.15875 

744769 

642735647 

29.3769 

809 

1.23609 

654481 

529475129 

28.4429 

864 

1.15741 

746496 

644972544 

29-3939 

810 

1.23457 

656100 

53I44IOOO 

28.4605 

865 

1.15607 

748225 

647214625 

29.4109 

811 

1  -23305 

657721 

5334II73I 

28.4781 

866 

1.15473 

749956 

649461896 

29.4279 

812 

L23I53 

659344 

535387328 

28.4956 

867 

1.15340 

751689 

651714363 

29.4449 

813 

I.23OOI 

660969 

537367797 

28.5132 

868 

1.15207 

753424 

653972032 

29.4618 

814 

1.22850 

662596 

539353M4 

28.5307 

869 

1.15075 

755l6i 

656234909 

29.4788 

815 

1.22699 

664225 

541343375 

28.5482 

870 

1.14943 

756900 

658503000 

29.4958 

816 

1.22549 

665856 

543338496 

28.5657 

871 

1.14811 

758641 

660776311 

295127 

817 

1.22399 

667489 

54533851  3 

28.5832 

872 

1.14679 

760384 

663054848 

29.5296 

818 

1.22249 

669124 

547343432 

28.6007 

873 

1.14548 

762129 

665338617 

29.5466 

819 

1.  22100 

670761 

549353259 

28.6182 

874 

1.14416 

763876 

667627624 

29-5635 

820 

I.2I95I 

672400 

551368000 

28.6356 

875 

1.14286 

765625 

669921875 

29.5804 

821 

1.21803 

674041 

553387661 

28.6531 

876 

1.14155 

767376 

672221376 

29-5973 

822 
823 

I.2I655 

I.2T507 

675684 
677329 

555412248 
557441767 

28.6705 
28.6880 

877 
878 

1.14025 
I-I3895 

769129 
770884 

674526133 
676836152 

29.6142 
29.63  1  1 

824 

L2I359 

678976 

559476224 

28.7054 

879 

1.13766 

772641 

679I5I439 

29.6479 

825 

I.2I2I2 

680625 

561515625 

28.7228 

880 

1.13636 

774400 

681472000 

29.6648 

826 

I.2IO65 

682276 

563559976 

28.7402 

88  1 

1.13507 

776161 

683797841 

29.6816 

827 

I.209I9 

683929 

565609283 

28.7576 

882 

I.I3379 

777924 

686128968 

29.6985 

828 

1.20773 

685584 

567663552 

28.7750 

883 

1.13250 

779689 

688465387 

29-7153 

829 

1.20627 

687241 

569722789 

28.7924 

884 

1.13122 

781456 

690807104 

29.7321 

830 

1.20482 

688900 

571787000 

28.8097 

885 

1.12994 

783225 

693!54i25 

29-7489 

831 

1.20337 

690561 

573856191 

28.8271 

886 

1.12867 

784996 

695506456 

29.7658 

832 

I.2OI92 

692224 

575930368 

28.8444 

887 

1.12740 

786769 

697864103 

29.7825 

833 

1.20048 

693889 

578009537 

28.8617 

888 

1.12613 

788544 

700227072 

29-7993 

834 

1.19904 

695556 

580093704 

28.8791 

889 

1.12486 

790321 

702595369 

29.8161 

SMITHSONIAN  TABLES. 


TABLE  6   (continued).  21 

VALUES   OF   RECIPROCALS,  SQUARES,  CUBES,  AND   SQUARE    ROOTS 
OF   NATURAL    NUMBERS. 


n 

lOOO.jj 

w2 

»3 

*• 

n 

IOOO.£ 

»2 

«3 

v« 

890 

1.12360 

792100 

704969000 

29.8329 

945 

1.05820 

893025 

843908625 

30.7409 

891 

1.12233 

793881 

707347971 

29.8496 

946 

1.05708 

894916 

846590536 

30.7571 

892 

i.  12108 

795664 

709732288 

29.8664 

947 

1.05597 

896809 

849278123 

30-7734 

893 

1.11982 

797449 

7I2I2I957 

29.8831 

948 

1.05485 

898704 

851971392 

30.7896 

894 

1.11857 

799236 

714516984 

29.8998 

949 

1.05374 

900601 

854670349 

30.8058 

895 

1.11732 

801025 

7I69I7375 

29.9166 

950 

1.05263 

902500 

857375000 

30.8221 

896 

1.11607 

802816 

719323136 

29-9333 

951 

1.05152 

904401 

860085351 

30.8383 

897 

1.11483 

804609 

721734273 

29.9500 

952 

1.05042 

906304 

862801408 

30.8545 

898 

I-II359 

806404 

724150792 

29.9666 

953 

1.04932 

908209 

865523177 

30.8707 

899 

1.11235 

808201 

726572699 

29-9833 

954 

1.04822 

9IOII6 

868250664 

30.8869 

900 

i.  inn 

810000 

729000000 

30.0000 

955 

1.04712 

9I2O25 

870983875 

30.9031 

901 

1.10988 

811801 

731432701 

30.0167 

956 

1.04603 

913936 

873722816 

30.9192 

902 

1.10865 

813604 

733870808 

30-0333 

957 

1.04493 

915849 

876467493 

30.9354 

9°3 

1.10742 

815409 

7363*4327 

30.0500 

958 

1.04384 

917764 

879217912 

30.9516 

904 

1.10619 

817216 

738763264 

30.0666 

959 

1.04275 

919681 

881974079 

30.9677 

905 

1.10497 

819025 

741217625 

30.0832 

960 

1.04167 

921600 

884736000 

30.9839 

906 

1-10375 

820836 

743677416 

30.0998 

961 

1  .04058 

923521 

887503681 

31.0000 

907 

1.10254 

822649 

746142643 

30.1164 

962 

1.03950 

925444 

890277128 

31.0161 

908 

1.10132 

824464 

748613312 

30.1330 

963 

1.03842 

927369 

893056347 

31.0322 

909 

I.IOOII 

826281 

751089429 

30.1496 

964 

1.03734 

929296 

895841344 

31.0483 

910 

1.09890 

828100 

753571000 

30.1662 

965 

1.03627 

931225 

898632125 

31.0644 

911 

1.09769 

829921 

756058031 

30.1828 

966 

1.03520 

933^6 

901428696 

31.0805 

912 

1.09649 

831744 

758550528 

30-I993 

967 

1.03413 

935089 

904231063 

31.0966 

9*3 
914 

1.09529 
1.09409 

833569 
835396 

761048497 
76355^44 

30.2159 
30.2324 

968 
969 

1.03306 
1.03199 

937024 
938961 

907039232 
909853209 

31.1127 
31.1288 

915 

1.09290 

837225 

766060875 

30.2490 

970 

1.03093 

940900 

912673000 

31.1448 

916 

1.09170 

839056 

768575296 

30-2655 

971 

1.02987 

942841 

9I54986II 

31.1609 

917 

1.09051 

840889 

771095213 

3O.282O 

972 

1.02881 

944784 

918330048 

31.1769 

918 
919 

1.08932 
1.08814 

842724 
844561 

773620632 
776I5I559 

30.2985 
30.3150 

973 
974 

1.02775 

1.02669 

946729 
948676 

92II673I7 
924010424 

31.1929 
31.2090 

920 

1.08696 

846400 

778688000 

30.3315 

975 

1.02564 

950625 

926859375 

31.2250 

921 

1.08578 

848241 

781229961 

30.3480 

976 

1.02459 

952576 

929714176 

31.2410 

922 
923 

1.08460 
1.08342 

850084 
851929 

783777448 
786330467 

30-3645 
30.3809 

977 
978 

1.02354 
1.02249 

954529 
956484 

932574833 
935441352 

31.2570 
31.2730 

924 

1.08225 

853776 

788889024 

30.3974 

979 

1.02145 

958441 

9383*3739 

31.2890 

925 

1.  08  1  08 

855625 

79M53I25 

30.4138 

980 

1.02041 

960400 

941  192000 

31-3050 

926 

1.07991 

857476 

794022776 

30.4302 

981 

1.01937 

962361 

944076141 

31.3209 

927 

1.07875 

859329 

796597983 

30.4467 

982 

1.01833 

964324 

946966168 

3  *  -3369 

928 
929 

1.07759 
1.07643 

861184 
863041 

799178752 
801765089 

30.4631 
30.4795 

983 
984 

1.01729 
1.01626 

966289 
968256 

949862087 
952763904 

3I-3528 
31.3688 

930 

1.07527 

864900 

804357000 

30-4959 

985 

1.01523 

970225 

955671625 

3I-3847 

93  l 

1.07411 

866761 

806954491 

3°-  5  i  23 

986 

1.01420 

972196 

958585256 

31.4006 

932 

1.07296 

868624 

809557568 

30.5287 

987 

1.01317 

974169 

961504803 

31.4166 

933 

1.07181 

870489 

812166237 

30.545o 

988 

1.01215 

976144 

964430272 

3M325 

934 

1.07066 

872356 

814780504 

30.5614 

989 

I.OIII2 

978121 

967361669 

31.4484 

935 

1.06952 

874225 

817400375 

30.5778 

990 

I.OIOIO 

980100 

970299000 

3  r  -4643 

936 
937 

1.06838 
1.06724 

876096 
877969 

820025856 
822656953 

30-594I 
30.6105 

991 
992 

1.00908 

1.00806 

982081 
984064 

973242271 
976191488 

31.4802 
31.4960 

938 
939 

1.06610 
1.06496 

879844 
881721 

825293672 
827936019 

30.6268 
30.6431 

993 
994 

1.00705 

1.00604 

986049 
988036 

979146657 
982107784 

3i-5ii9 

3I-5278 

940 

1.06383 

883600 

830584000 

30.6594 

995 

1.00503 

990025 

985074875 

3  *  -5436 

941 

1.06270 

885481 

833237621 

30-6757 

996 

1.00402 

992016 

988047936 

3J-5595 

942 

1.06157 

887364 

835896888 

30.6920 

997 

1.00301 

994009 

991026973 

31-5753 

943 

1.06045 

889249 

838561807 

30.7083 

998 

1.00200 

996004 

994011992 

31-59" 

944 

1.05932 

891136 

841232384 

30.7246 

999 

1.  00  1  00 

998001 

997002999 

31.6070 

SMITHSONIAN  TABLES. 


22 


TABLE  7. 
LOGARITHMS. 


N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

100 

oooo 

0004 

0009 

0013 

0017 

0022 

0026 

0030 

°°35 

0039 

0043 

101 
102 

0043 
0086 

0048 
0090 

0052 
0095 

0056 
0099 

0060 
0103 

0065 
OIO7 

0069 
oin 

0073 
0116 

0077 

0120 

0082 
0124 

0086 
0128 

103 

0128 

0*33 

0*37 

0141 

0145 

0149 

0154 

0158 

Ol62 

0166 

0170 

104 

0170 

0*75 

0179 

0183 

0187 

0191 

oi9S 

0199 

O204 

0208 

0212 

105 

106 

O2I2 
0253 

0216 

0257 

0220 
O26l 

0224 
0265 

0228 
0269 

0233 
0273 

0237 
0278 

0241 
0282 

0245 
0286 

0249 
0290 

0253 
0294 

107 

0294 

0298 

0302 

0306 

0310 

0314 

0318 

0322 

0326 

033° 

°334 

1  08 

0334 

0338 

0342 

0346 

0350 

0354 

0358 

0362 

0366 

0370 

0374 

109 

0374 

0378 

0382 

0386 

0390 

0394 

0398 

0402 

0406 

0410 

0414 

110 

0414 

0418 

0422 

0426 

0430 

0434 

0438 

0441 

0445 

0449 

°453 

in 

°453 

0457 

0461 

0465 

0469 

0473 

0477 

0481 

0484 

0488 

0492 

112 

0492 

0496 

0500 

0504 

0508 

0512 

°5J5 

0519 

0523 

0527 

°53I 

"3 

0531 

0535 

0538 

0542 

0546 

0550 

0554 

0558 

0561 

0565 

0569 

114 

0569 

°573 

0577 

0580 

0584 

0588 

0592 

0596 

0599 

0603 

0607 

115 

0607 

0611 

0615 

0618 

0622 

0626 

0630 

0633 

0637 

0641 

0645 

116 

0645 

0648 

0652 

0656 

0660 

0663 

0667 

0671 

0674 

0678 

0682 

"7 

0682 

0686 

0689 

0693 

0697 

0700 

0704 

0708 

0711 

0715 

0719 

118 

0719 

0722 

0726 

0730 

0734 

0737 

0741 

0745 

0748 

0752 

°75S 

119 

0755 

0759 

0763 

0766 

0770 

0774 

0777 

0781 

0785 

0788 

0792 

120 

0792 

0795 

0799 

0803 

0806 

0810 

0813 

0817 

0821 

0824 

0828 

121 

0828 

0831 

0835 

0839 

0842 

0846 

0849 

0853 

0856 

0860 

0864 

122 

0864 

0867 

0871 

0874 

0878 

O88l 

0885 

0888 

0892 

0896 

0899 

I23 

0899 

0903 

0906 

0910 

0913 

0917 

0920 

0924 

0927 

0931 

0934 

124 

0934 

0938 

0941 

0945 

0948 

0952 

0955 

0959 

0962 

0966 

0969 

125 

0969 

0973 

0976 

0980 

0983 

0986 

0990 

0993 

0997 

IOOO 

1004 

126 

1004 

1007 

ion 

1014 

1017 

1021 

1024 

1028 

1031 

I035 

1038 

127 

1038 

1041 

1045 

1048 

1052 

IO55 

I059 

1062 

I065 

1069 

1072 

128 

1072 

1075 

1079 

1082 

1086 

1089 

1092 

1096 

1099 

1103 

1106 

129 

1106 

1109 

1113 

ni6 

1119 

1123 

1126 

1129 

"33 

1136 

"39 

130 

"39 

"43 

1146 

1149 

"53 

1156 

"59 

1163 

1166 

1169 

"73 

131 

"73 

1176 

"79 

1183 

1186 

1189 

"93 

1196 

"99 

1  202 

1206 

132- 

1206 

1209 

1212 

1216 

1219 

1222^ 

1225 

1229 

1232 

I235 

1239 

133 

1239 

1242 

1245 

1248 

1232 

I2S5 

1258 

1261 

1265 

1268 

1271 

134 

1271 

1274 

I278 

1281 

1284 

1287 

1290 

1294 

1297 

1300 

J3°3 

135 

1303 

1307 

1310 

1313 

1316 

1319 

1323 

1326 

1329 

,332 

1335 

136 

1335 

1339 

1342 

U45 

1348 

13^1 

1358 

1361 

1364 

^67 

139 

1367 
1399 
1430 

1370 
1402 
H33 

1374 
1405 

1436 

1377 
1408 
1440 

1380 
1411 
1443 

1383 
1414 
1446 

1418 
1449 

1389 
1421 
MS2 

1392 
1424 

1455 

1396 
1427 

1458 

1399 
143° 
1461 

140 

1461 

1464 

1467 

1471 

H74 

1477 

1480 

1483 

1486 

1489 

1492 

141 

1492 

'495 

I498 

1501 

1504 

1508 

'5" 

15*4 

1517 

1520 

1523 

142 

1523 

1526 

1529 

1532 

1535 

1538 

i54i 

1544 

1547 

1550 

1553 

143 

'553 

1556 

1559 

1562 

1565 

*5^9 

1572 

i|75 

'578 

1581 

1584 

144 

1584 

I5»7 

I59° 

1593 

1596 

1599 

1602 

1605 

1608 

IOII 

1614 

145 

1614 

1617 

1620 

1623 

1626 

1629 

1632 

l635 

1638 

1641 

1644 

146 

1644 

1647 

1649 

1652 

1655 

1658 

1661 

1664 

1667 

1670 

1673 

147 

1673 

1676 

1679 

1682 

1685 

l688 

1691 

1694 

1697 

1700 

-1703 

148 

1703 

1706 

1708 

1711 

1714 

1717 

1720 

1723 

1726 

1729 

1732 

149 

1732 

1735 

1738 

1741 

1744 

1746 

1749 

1752 

1755 

1758 

1761 

SMITHSONIAN  TABLES. 


TABLE  7  (continued). 

LOGARITHMS. 


N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

150 

1761 

1764 

1767 

1770 

1772 

I77S 

1778 

1781 

1784 

1787 

1790 

1790 

J793 

1796 

1798 

1801 

1804 

1807 

1810 

1813 

1816 

1818 

1 

1818 
1847 

1821 
1850 

1824 
1853 

1827 
1855 

1830 

1858 

1833 
1861 

1836 
1864 

1838 
1867 

1841 
1870 

1844 
1872 

1847 
1875 

154 

1875 

1878 

1881 

1884 

1886 

1889 

1892 

1895 

1898 

1901 

1903 

155 

1903 

1906 

1909 

1912 

I9T5 

1917 

1920 

1923 

1926 

1928 

'931 

156 

157 

I931 
1959 

1934 
1962 

1965 

1940 
1967 

1942 
1970 

'945 
J973 

1948 
1976 

'951 
1978 

1953 
1981 

1956 
1984 

1959 
1987 

158 

1987 

1989 

1992 

1995 

1998 

2000 

2003 

2006 

2009 

2OII 

2014 

159 

2014 

2017 

2019 

2O22 

2O25 

2028 

2030 

2033 

2036 

2038 

2041 

160 

2041 

2044 

2047 

2049 

2052 

2055 

2057 

2060 

2063 

2066 

2068 

161 

2068 

2071 

2074 

2076 

2079 

2082 

2084 

2087 

2090 

2092 

2095 

L  162 

2095 

2098 

2IOI 

2103 

2106 

2IO9 

2III 

2114 

2117 

2119 

2122 

If  l63 

2122 

2125 

2127 

2130 

2133 

2135 

2I38 

2140 

2143 

2146 

2148 

164 

2148 

2151 

2154 

2156 

2159 

2l62 

2164 

2167 

2170 

2173' 

2175 

165 

2175 

2177 

2180 

2183 

2185 

2188 

2191 

2193 

2196 

2198 

22OI 

166 

22OI 

2204 

2206 

22O9 

2212 

2214 

2217 

2219 

2222 

2225 

2227 

167 

2227 

2230^ 

2232 

2235 

2238 

224O 

2243 

2245 

2248 

2251 

2253 

168 

2253 

2256 

2258 

2261 

2263 

2266 

2269 

2271 

2274 

2276 

2279 

169 

2279 

2281 

2284 

2287 

2289 

2292 

2294 

2297 

2299 

2302 

2304 

170 

2304 

2307 

23IO 

23I2 

2315 

2317 

2320 

2322 

2325 

2327 

2330 

171 

2330 

2333 

2335 

2338 

2340 

2343 

2345 

2348 

2350 

2353 

2355 

172 

2355 

2358 

2360 

2363 

2365 

2368 

2370 

2373 

2375 

2378 

2380 

173 

2380 

2383 

2385 

2388 

2390 

2393 

2395 

2398 

2400 

2403 

2405 

174 

2405 

2408 

24IO 

24U 

2415 

2418 

2420 

2423 

2425 

2428 

2430 

17? 

2430 

2433 

2435 

2438 

2440 

2443 

2445 

2448 

2450 

2453 

2455 

176 

177 

2480 

2458 
2482 

2460 
2485 

2463 
2487 

2465 
2490 

2467 
2492 

2470 
2494 

2472 
2497 

2475 
2499 

2477 
2502 

2480 
2504 

178 
179 

2504 
2529 

2507 
2531 

2509 
2533 

25I2 
2536 

2514 
2538 

2516 
2541 

2519 

2543 

2521 
2545 

2524 
2548 

2526 
2550 

2529 
2553 

ia° 

2553 

2555 

2558 

2560 

2562 

2565 

2567 

2570 

2572 

2574 

2577 

III 
183 
184 

2|77 
26OI 
2625 
2648 

2579 
2603 
2627 
2651 

2582 
2605 
2629 
2653 

2632 
2655 

2586 
26lO 
2634 
2658 

2589 
2613 
2636 
2660 

2591 
2615 

2662 

2594 
2617 
2641 
2665 

2643 
2667 

2598 
2622 
2646 
2669 

2601 
2625 
2648 
2672 

185 

2672 

2674 

2676 

2679 

268l 

2683 

2686 

2688 

2690 

2693 

2695 

186 

2695 

2697 

2700 

27O2 

2704 

2707 

2709 

2711 

2714 

2716 

27l8 

187 

27l8 

2721 

2723 

2725 

2728 

2730 

2732 

2735 

2737 

2739 

2742 

188 
189 

2742 
2765 

2744 
2767 

2746 
2769 

2749 
2772 

2751 
2774 

2753 
2776 

2755 
2778 

275» 
2781 

2760 
2783 

2762 
2785 

2765 
2788 

190 

191 

2788 
28lO 

2790 
2813 

2792 
28lC 

2794 
2817 

2797 
2819 

2799 

2822 

2801 
2824 

2804 
2826 

2806 

2828 

2808 
2831 

28lO 
2833 

192 
J93 

2833 
2856 

2835 
2858 

2838 

2840 
2862 

2842 
2865 

2844 
2867 

2869 

2849 
2871 

2851 
2874 

2853 
2876 

2856 
2878 

194 

2878 

2880 

2882 

2885 

2887 

2889 

2891 

2894 

2896 

2898 

2900 

195 

_ 

2900 

2903 

2905 

2907 

2909 

2911 

2914 

2916 

2918 

2920 

2923 

196 

2923 

2925 

2927 

2929 

2931 

2934 

2936 

2938 

2940 

2942 

2945 

2945 

2947 

2949 

2951 

2953 

2956 

2958 

2960 

2962 

2964 

2967 

198 

2967 

2969 

2971 

2973 

297S 

2978 

2980 

2982 

2984 

2986 

2989 

199 

2991 

2993 

2995 

2997 

2999 

3002 

3004 

3006 

3008 

3010 

SMITHSONIAN  TABLES. 


TABLE  8. 
LOGARITHMS. 


N 


10 

ii 

12 
13 

14 

15 

16 

17 
18 


20 

21 
22 

23 
24 

25 

26 
27 
28 
29 

30 

3i 
32 
33 
34 

35 

36 


39 

40 

4i 

42 

43 

44 

45 

46 
47 
48 

49 

50 

Si 

52 
53 
54 


8        9 


0000 

0414 
0792 

"39 
1461 

1761 
2041 
2304 
2553 
2788 

3010 
3222 

3424 
3617 
3802 

3979 
415° 
43H 
4472 
4624 

4771 
4914 


5315 


6721 
6812 
6902 

6990 
7076 
7160 
7243 
7324 


0043  0086  0128 

0453  0492  0531 

0828  0864  0899 

1173  1206  1239 

1492  1523  1553 

1790  1818  1847 

2068   2095  2122 

233°  2355  2380 

2577   2601  2625 

2810  2833  2856 

3032   3OC4  3075 

3243  3263  3284 

3444  3464  3483 

3636  3655  3674 

3820  3838  3856 

3997  4014  4031 

4166  4183  4200 

433°  4346  4362 

4487  4502  4518 

4639  4654  4669 

4786  4800  4814 

4928  4942  4955 

5065  5079  5092 

5198  5211  5224 

5328  5340  5353 

5453  5465  5478 

5575  5587  5599 

5694  5705  57i7 

5809  5821  5832 

5922  5933  5944 

6031  6042  6053 

6138  6149  6160 

6243  6253  6263 

6345  6355  6365 

6444  6454  6464 

6542  6551  6561 

6637  6646  6656 

673°  6739  6749 

6821  6830  6839 

6911  6920  6928 

6998  7007  7016 

7084  7093  7101 

7168  7177  7185 

7251  7259  7267 

7332  7340  7348 


OI7O  O2I2  0253 

0569  0607  0645 

0934  0969  1004 

I27I  1303  1335 

1584  IOI4  1644 

1875  19°3  I93T 

2148  2-175  22OI 

2405  2430  2455 

2648  2672  2695 

2878  29OO  2923 

3096  3118  3139 

3304  3324  3345 

3502  3522  3541 

3692  3711  3729 

3874  3892  3909 

4048  4065  4082 

4216  4232  4249 

4378  4393  4409 

4533  4548  4564 

4683  4698  4713 

4829  4843  4857 

4969  4983  4997 

5I05  5IJ9  5*32 

5237  5250  5263 

5366  5378  5391 

5490  5502  5514 

5611  5623  563*5 

5729  5740  5752 

5843  58 


5955 


5866 
5977 


6064  6075  6°85 

6170  6180  6191 

6274  6284  6294 

6375  6385  6395 

6474  6484  6493 

6571  6580  6590 

6665  6675  6684 

6758  6767  6776 

6848  6857  6866 

6937  6946  6955 

7024  7033  7042 

7110  7118  7126 

7193  7202  7210 

7275  7284  7292 

7356  7364  7372 


0294  0334  0374 

0682  0719  0755 

1038  1072  1106 

1367  1399  M30 

1673  J703  1732 

1959  1987  2014 

2227  2253  2270 

2480  2504  2529 

2718  2742  2765 

2945  2967  2989 

3160  3181  3201 

3365  3385  3404 

356o  3579  3598 

3747  3766  3784 

3927  3945  3962 

4099  4116  4133 

4265  4281  4298 

4425  4440  4456 

4579  4594  4609 

4728  4742  4757 

4871  4886  4900 

5011  5024  5038 

5r45  5J59  5J72 

5276  5289  5302 

5403  5416  5428 

5527  5539  555i 

5647  5658  5670 

5763  5775  5786 

5877  5888  5899 

5988  5999  6010 

6096  6107  6117 

6201  6212  6222 

6304  6314  6325 

6405  6415  6425 

65°3  65J3  6522 

6599  6609  6618 

6693  6702  6712 

6785  6794  6803 

6875  6884  6893 

6964  6972  6981 

7050  7059  7067 


721  ^722  7235 
7300  7308  7316 
738o  7388  7396 


P.P. 


12 


10 
10 


SMITHSONIAN  TABLES. 


TABLE  8  (continued). 
LOGARITHMS. 


N. 

0     123     456     789 

] 

P.  F 

1 

2 

3 

4 

5 

55 

7404   7412  7419  7427   7435  7443  7451   7459  7466  7474 

2 

2 

3 

4 

56 

7482   7490  7497  7505   7513  7520  7528   7535  7543  7551 

2 

2 

3 

4 

57 

7559   7566  7574  7582   7589  7597  7604   7612  7619  7627 

2 

2 

3 

4 

58 

7634   7642  7649  7657   7664  7672  7679   7686  7694  7701 

2 

3 

4 

59 

7709   7716  7723  7731   7738  7745  7752   7760  7767  7774 

2 

3 

4 

60 

61 

7782   7789  7796  7803   7810  7818  7825   7832  7839  7846 
7853   7860  7868  7875   7882  7889  7896   7903  7910  7917 

2 

2 

3 

3 

4 
4 

62 

7924   793  i  7938  7945   7952  7959  7966   7973  798°  7987 

2 

3 

3 

63 

7993   8000  8007  8014   8021  8028  8035   8041  8048  8055 

2 

3 

3 

64 

8062   8069  8075  8082   8089  8096  8102   8109  8116  8122 

2 

3 

3 

65 

8129   8136  8142  8149   8156  8162  8169   8176  8182  8189 

2 

3 

3 

66 

8195   8202  8209  8215   8222  8228  8235   8241  8248  8254 

2 

3 

3 

67 
68 
69 

8261   8267  8274  8280   8287  8293  8299   8306  8312  8319 
8325   8331  8338  8344   8351  8357  8363   8370  8376  8382 
8388   8395  8401  8407   8414  8420  8426   8432  8439  8445 

2 
2 
2 

3 
3 
3 

3 
3 
3 

70 

8451   8457  8463  8470   8476  8482  8488   8494  8500  8506 

2 

2 

3 

71 

8513   8519  8525  8531   8537  8543  8549   8555  8561  8567 

2 

2 

3 

72 
73 

8573   8579  8585  8591   8597  8603  8609   8615  8621  8627 
8633   8639  8645  8651   8657  8663  8669   8675  8681  8686 

2 
2 

2 

2 

3 
3 

74 

8692   8698  8704  8710   8716  8722  8727   8733  8739  8745 

2 

2 

3 

75 

8751   8756  8762  8768   8774  8779  8785   8791  8797  8802 

2 

2 

3 

76 

8808   8814  8820  8825   8831  8837  8842   8848  8854  8859 

2 

2 

3 

77 

8865   8871  8876  8882   8887  8893  8899   8904  8910  8915 

2 

2 

3 

78 

8921   8927  8932  8938   8943  8949  8954   8960  8965  8971 

2 

2 

3 

79 

8976   8982  8987  8993   8998  9004  9009   9015  9020  9025 

2 

2 

3 

80 

9031   9036  9042  9047   9053  9058  9063   9069  9074  9079 

2 

2 

3 

81 

9085   9090  9096  9101   9106  9112  9117   9122  9128  9133 

2 

2 

3 

82 

9138   9143  9149  9154   9159  9165  9170   9175  9180  9186 

2 

2 

3 

83 

9191   9196  9201  9206   9212  9217  9222   9227  9232  9238 

2 

2 

3 

84 

9243   9248  9253  9258   9263  9269  9274   9279  9284  9289  ( 

2 

2 

3 

85 

9294   9299  9304  9309   9315  9320  9325   9330  9335  9340 

2 

2 

3 

86 

9345   9350  9355  936°   93^5  937°  9375   938°  9385  939° 

2 

2 

3 

87 

9395   9400  9405  94io   9415  9420  9425   9430  9435  9440 

o 

2 

2 

88 

9445   9450  9455  9460   9465  9469  9474   9479  9484  9489 

0 

2 

2 

89 

9494   9499  9504  9509   9513  9518  9523   9528  9533  9538 

0 

2 

2 

90 

9542   9547  9552  9557   95^2  9566  957i   9576  9581  95^6 

o 

2 

2 

91 

959°   9595  9600  9605   9609  9614  9619   9624  9628  9633 

o 

2 

2 

92 

9638   9643  9647  9652   9657  9661  9666   9671  9675  9680 

o 

2 

2 

93 

9685   9689  9694  9699   9703  9708  9713   9717  9722  9727 

o 

2 

2 

94 

9731   9736  974i  9745   9750  9754  9759   9763  9768  9773 

0 

2 

2 

95 

9777   9782  9786  9791   9795  9800  9805   9809  9814  9818 

.0 

2 

2 

96 

9823   9827  9832  9836   9841  9845  9850   9854  9859  9863 

o 

2 

2 

97 

9868   9872  9877  9881   9886  9890  9894  •  9899  9903  9908 

o 

2 

2 

98 

9912   9917  9921  9926   9930  9934  9939   9943  9948  9952 

0 

2 

2 

99 

9956   9961  9965  9969   9974  9978  9983   9987  9991  9996 

0 

2 

2 

SMITHSONIAN  TABLES. 


26 


TABLE  9. 
ANTILOGARITHMS. 


Onoo       456       7     ft     Q 

] 

3.  p 

JL       «       O           Tt       *J       W           /        O       *r 

1 

2 

3 

4 

5 

.00 

IOOO     IOO2   IOO5   IOO7     IOO9  IOI2  IOI4     IOl6  IOI9  IO2I 

0 

o 

.01 

1023    1026  1028  1030   1033  1035  IO38    IO4°  IO42  IO45 

o 

0 

.02 

1047   I05°  I052  I054   I057  I059  Io62   Io64  Io67  Io69 

o 

o 

•°3 

1072   1074  1076  1079   1081  1084  1086   1089  1091  1094 

0 

0 

.04 

1096     IO99  IIO2   IIO4     IIO7   IIO9  1  1  12     III4  III7   III9 

o 

I 

.05 

1122   1125  1127  1130   1132  1135  1138   1140  1143  IT46 

0 

I 

.06 

1148   1151  1153  1156   1159  1161  1164   1167  1169  1172 

o 

I 

.07 

1175   1178  1180  1183   1186  1189  1191    1194  1197  1199 

o 

I 

.08 

I2O2     I2O5   I2O8   I2II     1213   I2l6   1219     1222   1225   1227 

0 

I 

.09 

1230     1233  1236  1239     1242  1245   1247     1250  1253  1256 

o 

I 

i 

.10 

1259     1262   1265   1268     1271   1274  1276     1279  1282   1285 

o 

I 

i 

.11 

1288     1291   1294  1297     1300  1303  1306     1309  1312  1315 

0 

I 

2 

.12 

1318     1321   1324  1327     1330  1334  1337     1340  1343   1346 

o 

I 

2 

•13 

1349     1352   1355   1358     1361   1365   1368     1371   1374  1377 

o 

I 

2 

.14 

1380     1384  1387   1390     1393   1396  1400     1403  1406  1409 

o 

I 

2 

.15 

1413     I4l6  1419  1422     1426  1429  1432     1435  1439  1442 

o 

I 

2 

.16 

1445   *449  US2  M55   J459  1462  1466   1469  1472  1476 

o 

I 

2 

•17 
.18 

1479   J483  J486  1489   1493  M96  1500   1503  1507  1510 
i5H   15*7  *521  *524   i528  I531  ^535   J538  *542  1545 

0 

o 

I 

2 
2 

.19 

1549   1552  1556  1560   1563  1567  1570   1574  1578  1581 

o 

1 

2 

.20 

J585   *589  T592  T59^   1600  1603  1607   1611  1614  1618 

o 

I 

i 

2 

.21 

1622   1626  1629  1633   1637  1641  1644   1648  1652  1656 

o 

I 

2 

2 

.22 

1660   1663  1667  1671   1675  J679  1683   1687  1690  1694 

o 

I 

2 

2 

•23 

1698   1702  1706  1710   1714  1718  1722   1726  1730  1734 

0 

I 

2 

2 

.24 

1738   1742  1746  1750   1754  1758  1762   1766  1770  1774 

o 

1 

2 

2 

.25 

1778   1782  1786  1791    1795  J799  l8°3   l8°7  l8ir  l8l6 

0 

I 

2 

2 

.26 

1820   1824  1828  1832   1837  1841  1845   1849  1854  1858 

o 

I 

2 

2 

.27 

1862   1866  1871  1875   l879  l884  l888   l892  l897  I9°I 

o 

I 

2 

2 

.28 

1905   1910  1914  1919   1923  1928  1932   1936  1941  1945 

0 

I 

2 

2 

.29 

J95°   1954  T959  J9^3   I9^8  *972  J977   I982  J98^  J99* 

o 

I 

2 

2 

.30 

•3i 

1995   2000  2004  2009   2014  2018  2023   2028  2032  2037 
2042   2046  2051  2056   2061  2065  2070   2075  2°8°  2084 

0 

o 

I 
I 

2 
2 

2 

2 

•32 

2089   2094  2099  2104   2109  2113  2118   2123  2128  2133 

o 

I 

2 

2 

•33 

2138   2143  2148  2153   2158  2163  2168   2173  2178  2183 

o 

I 

2 

2 

•34 

2188   2193  2198  2203   2208  2213  2218   2223  2228  2234 

I 

1 

2 

2 

3 

.35 

2239   2244  2249  2254   2259  2265  2270   2275  2280  2286 

I 

2 

2 

3 

•36 

2291   2296  2301  2307   2312  2317  2323   2328  2333  2339 

I 

2 

2 

3 

2344   2350  2355  2360   2366  2371  2377   2382  2388  2393 

I 

2 

2 

3 

.38 

2399   2404  2410  2415   2421  2427  2432   2438  2443  2449 

I 

2 

2 

3 

•39 

2455   2460  2466  2472   2477  2483  2489   2495  25°°  25°6 

I 

2 

2 

3 

.40 

2512   2518  2523  2529   2535  2541  2547   2553  2559  2564 

I 

2 

2 

3 

.41 

2570   2576  2582  2588   2594  2600  2606   2612  2618  2624 

I 

2 

2 

3 

.42 

2630   2636  2642  2649   2655  266r  2667   2673  2^79  2685 

I 

2 

2 

3 

•43 

2692   2698  2704  2710   2716  2723  2729   2735  2742  2748 

I 

2 

3 

3 

.44 

2754   2761  2767  2773   2780  2786  2793   2799  2805  2§I2 

1 

2 

3 

3 

.45 

2818   2825  2831  2838   2844  285r  2858   28^4  287r  2877 

I 

2 

3 

3 

.46 

2884   2891  2897  2904   2911  2917  2924   2931  2938  2944 

I 

2 

3 

3 

•47 

2951   2958  2965  2972   2979  2985  2992   2999  3006  3013 

I 

2 

0 

3 

.48 

3020   3027  3034  3041   3048  3055  3062   3069  3076  3083 

I 

2 

3 

4 

•49 

3090   3097  3105  3112   3119  3126  3133   3141  3H8  3'55 

I 

2 

3 

4 

SMITHSONIAN  TABLES. 


TABLE  9  (continued). 

ANTILOGARITHMS. 


0     123     456     789 

] 

P.I 

> 

1 

2 

3 

4 

5 

.50 

3162   3170  3177  3184   3192  3199  3206   3214  3221  3228 

i 

2 

3 

4 

•Si 

3236   3243  3251  3258   3266  3273  3281   3289  3296  3304 

2 

2 

3 

4 

•52 

3311   33*9  3327  3334   3342  3350  3357   3365  3373  3381 

2 

2 

3 

4 

•53 

3388   3396  3404  3412   3420  3428  3436   3443  3451  3459 

2 

2 

3 

4 

•54 

3467   3475  3483  3491   3499  35°8  3516   3524  3532  3540 

2 

2 

3 

4 

.55 

3548   3556  3565  3573   358i  35§9  3597   3606  3614  3622 

2 

2 

3 

4 

.56 

363r   3639  3648  3656   3664  3673  3681   3690  3698  3707 

2 

3 

3 

4 

•57 

37i5   3724  3733  374i   3750  3758  3767   3776  3784  3793 

2 

3 

3 

4 

.58 

3802   3811  3819  3828   3837  3846  3855   3864  3873  3882 

2 

3 

4 

4 

•59 

3890   3899  3908  3917   3926  3936  3945   3954  39^3  3972 

2 

3 

4 

5 

.60 

3981   3990  3999  4009   4018  4027  4036   4046  4055  4064 

2 

3 

4 

5 

.61 

4074   4083  4093  4102   4111  4121  4130   4140  4150  4159 

2 

3 

4 

5 

.62 

4169   4178  4188  4198   4207  4217  4227   4236  4246  4256 

2 

3 

4 

5 

•63 
.64 

4266   4276  4285  4295   4305  4315  4325   4335  4345  4355 
4365   4375  4385  4395   44°6  44^  4426   4436  4446  4457 

2 
2 

3 
3 

4 
4 

5 
5 

.65 

.66 

4467   4477  4487  4498   4508  4519  4529   4539  4550  4560 
4571   4581  4592  4603   4613  4624  4634   4645  4656  4667 

2 
2 

3 
3 

4 
4 

5 
5 

.67 

4677   4688  4699  4710   4721  4732  4742   4753  4764  4775 

2 

3 

4 

5 

.68 

4786   4797  4808  4819   4831  4842  4853   4864  4875  4887 

2 

3 

4 

6 

•69 

4898   4909  4920  4932   4943  4955  4966   4977  4989  5000 

2 

3 

5 

6 

.70 

5012   5023  5035  5047   5058  5070  5082   5093  5105  5117 

2 

4 

5 

6 

•71 

5129   5140  5152  5164   5176  5188  5200   5212  5224  5236 

2 

4 

5 

6 

.72 

5248   5260  5272  5284   5297  5309  5321   5333  5346  5338 

2 

4 

5 

6 

•73 

5370   5383  5395  5408   5420  5433  5445   5458  5470  5483 

3 

4 

5 

6 

•74 

5495   55°8  552i  5534   5546  5559  5572   5585  5598  5610 

3 

4 

5 

6 

.75 

5623   5636  5649  5662   5675  5689  5702   5715  5728  5741 

3 

4 

5 

7 

.76 

5754   5768  5781  5794   5808  5821  5834   5848  5861  5875 

3 

4 

5 

7 

3 

5888   5902  5916  5929   5943  5957  5970   5984  5998  6012 
6026   6039  6053  6067   6081  6095  6109   6124  6138  6152 

3 
3 

4 
4 

7 
7 

•79 

6166   6180  6194  6209   6223  6237  6252   6266  6281  6295 

3 

4 

6 

7 

.80 

6310   6324  6339  6353   6368  6383  6397   6412  6427  6442 

! 

3 

4 

6 

7 

.81 

6457   6471  6486  6501   6516  6531  6546   6561  6577  6592 

2 

3 

5 

6 

8 

.82 

6607   6622  6637  6653   6668  6683  6699   6714  6730  6745 

2 

3 

5 

6 

8 

•83 

6761   6776  6792  6808   6823  6839  6855   6871  6887  6902 

2 

3 

5 

6 

8 

.84 

6918   6934  6950  6966   6982  6998  7015   7031  7047  7063 

2 

3 

5 

6 

8 

.85 

7079   7096  7112  7129   7145  7161  7178   7194  7211  7228 

2 

3 

5 

7 

8 

.86 

7244   7261  7278  7295   7311  7328  7345   7362  7379  7396 

2 

3 

5 

7 

8 

.87 
.88 

7413   7430  7447  7464   7482  7499  75J6   7534  755'  7568 
7586   7603  7621  7638   7656  7674  7691   7709  7727  7745 

2 
2 

3 
4 

5 
5 

7 

7 

9 
9 

.89 

7762   7780  7798  7816   7834  7852  7870   7889  7907  7925 

2 

4 

5 

7 

9 

.90 

7943   7962  7980  7998   8017  8035  8054   8072  8091  8110 

2 

4 

6 

7 

9 

.91 

8128   8147  8166  8185   8204  8222  8241   8260  8279  8299 

2 

4 

6 

8 

9 

.92 

83l8   8337  8356  8375   8395  8414  8433   8453  8472  8492 

2 

4 

6 

8 

10 

•93 

8511   8531  8551  8570   8590  8610  8630   8650  8670  8690 

2 

4 

6 

8 

10 

•94 

8710   8730  8750  8770   8790  8810  8831   8851  8872  8892 

2 

4 

6 

8 

10 

.95 

.96 

8913   8933  8954  8974   8995  9016  9036   9057  9078  9099 
9120   9141  9162  9183   9204  9226  9247   9268  9290  9311 

2 
2 

4 
4 

6 
6 

8 

8 

10 

II 

'9l 

9333   9354  9376  9397   9419  9441  9462   9484  9506  9528 

2 

4 

7 

9 

II 

.98 
•99 

955°   9572  9594  9616   9638  9661  9683   9705  9727  9750 
9772   9795  9817  9840   9863  9886  9908   9931  9954  9977 

2 
2 

4 

5 

7 

7 

9 
9 

II 
II 

SMITHSONIAN  TABLES. 


28 


TABLE  1O. 
ANTILOGARITHMS. 


0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

.900 

7943 

7945 

7947 

7949 

7951 

7952 

7954 

7956 

7958 

7960 

7962 

.901 

7962 

7963 

7965 

7967 

7969 

7971 

7973 

7974 

7976 

7978 

7980 

.902 

7980 

7982 

7984 

7985 

7987 

7989 

7993 

7995 

7997 

7998 

•9°3 

7998 

8000 

8002 

8004 

8006 

8008 

Sou 

8013 

8015 

8017 

.904 

8017 

8019 

8020 

8022 

8024 

8026 

8030 

8032 

8033 

8035 

.905 

8035 

8037 

8039 

8041 

8043 

8045 

8046 

8048 

8050 

8052 

8054 

.906 

8054 

8056 

8057 

8059 

8061 

8063 

8065 

8067 

8069 

8070 

8072 

.907 

8072 

8074 

8076 

8078 

8080 

8082 

8084 

8085 

8087 

8089 

8091 

.908 

8091 

8093 

8095 

8097 

8098 

8100 

8102 

8104 

8106 

8108 

8110 

.909 

8110 

8111 

8113 

8115 

8117 

8119 

8121 

8123 

8125 

8126 

8128 

.910 

8128 

8130 

8132 

8i34 

8136 

8138 

8140 

8141 

8143 

8145 

8147 

.911 

8147 

8149 

8151 

8i53 

8i55 

8156 

8158 

8168 

8162 

8164 

8166 

.912 

8166 

8168 

8170 

8171 

8i73 

8i75 

8i77 

8179 

8181 

8183 

8185 

•9*3 

8185 

8187 

8188 

8190 

8192 

8194 

8196 

8198 

8200 

8202 

8204 

.914 

8204 

8205 

8207 

8209 

8211 

8213 

8215 

8217 

8219 

8221 

8222 

.915 

8222 

8224 

8226 

8228 

8230 

8232 

8234 

8236 

8238 

8239 

8241 

.916 

8241 

8243 

8245 

8247 

8249 

8251 

8253 

8255 

8257 

8258 

8260 

.917 

8260 

8262 

8264 

8266 

8268 

8270 

8272 

8274 

8276 

8278 

8279 

.918 

8279 

8281 

8283 

8285 

8287 

8289 

8291 

8293 

8295 

8297 

8299 

.919 

8299 

8300 

8302 

8304 

8306 

8308 

8310 

8312 

8314 

8316 

8318 

.920 

.921 

8318 
8337 

8320 
8339 

8321 
8341 

8323 
8343 

8325 
8344 

8327 
8346 

8329 

8348 

833i 
8350 

8333 
8352 

8335 
8354 

8337 
8356 

.922 

8356 

8358 

8360 

8362 

8364 

8366 

8368 

8370 

8371 

8373 

8375 

•923 

8375 

8377 

8379 

8381 

8383 

8385 

8387 

8389 

8391 

8393 

8395 

.924 

8395 

8397 

8398 

8400 

8402 

8404 

8406 

8408 

8410 

8412 

8414 

.925 

8414 

8416 

8418 

8420 

8422 

8424 

8426 

8428 

8429 

8431 

8433 

.926 
.927 

8433 
8453 

8435 
8455 

8437 
8457 

8439 
8459 

8441 
8461 

8443 
8463 

8445 
8464 

8447 
8466 

8449 
8468 

8451 
8470 

8453 
8472 

.928 

8472 

8474 

8476 

8478 

8480 

8482 

8484 

8486 

8488 

8490 

8492 

.929 

8492 

8494 

8496 

8498 

8500 

8502 

8504 

8506 

8507 

8509 

8511 

.930 

•931 

8511 
8531 

8513 
8533 

8515 
8535 

851? 

8537 

8519 
8539 

8521 
8541 

8523 

8543 

8525 
8545 

8527 
8547 

8529 

8549 

853i 

8551 

•932 

8551 

8553 

8555 

8557 

8559 

8561 

8562 

8564 

8566 

8568 

8570 

•933 

8570 

8572 

8574 

8576 

8578 

8580 

8582 

8584 

8586 

8588 

8590 

•934 

8590 

8592 

8594 

8596 

8598 

8600 

8602 

8604 

8606 

8608 

8610 

.935 

8610 

8612 

8614 

8616 

8618 

8620 

8622 

8624 

8626 

8628 

8630 

•936 

8630 

8632 

8634 

8636 

8638 

8640 

8642 

8644 

8646 

8648 

8650 

•937 

8650 

8652 

8654 

8656 

8658 

8660 

8662 

8664 

8666 

8668 

8670 

•938 

8670 

8672 

8674 

8676 

8678 

8680 

8682 

8684 

8686 

8688 

8690 

•939 

8690 

8692 

8694 

8696 

8698 

8700 

8702 

8704 

8706 

8708 

8710 

.940 

8710 

8712 

8714 

8716 

8718 

8720 

8722 

8724 

8726' 

8728 

8730 

.941 

8730 

8732 

8734 

8736 

8738 

8740 

8742 

8744 

8746 

8748 

8750 

.942 

875° 

8752 

8754 

8756 

8758 

8760 

8762 

8764 

8766 

8768 

8770 

•943 

8770 

8772 

8774 

8776 

8778 

8780 

8782 

8784 

8786 

8788 

8790 

.944 

8790 

8792 

8794 

8796 

8798 

8800 

8802 

8804 

8806 

8808 

8810 

.945 

8810 

8813 

8815 

8817 

8819 

8821 

8823 

8825 

8827 

8829 

8831 

.946 

8831 

8833 

8835 

8837 

8839 

8841 

8843 

8845 

8847 

8849 

8851 

•947 

8851 

8853 

8855 

8857 

8839 

8861 

8863 

8865 

8867 

8870 

8872 

.948 

8872 

8874 

8876 

8878 

8880 

8882 

8884 

8886 

8888 

8890 

8892 

•949 

8892 

8894 

8896 

8898 

8900 

8902 

8904 

8906 

8908 

8910 

8913 

SMITHSONIAN  TABLES. 


TABLE   1  O  (continued). 
ANTILOGARITHMS, 


0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

.950 

•95  i 

8913 

8933 

8915 
8935 

8917 

8937 

8919 

8939 

8921 
8941 

8923 
8943 

8925 
8945 

8927 
8947 

8929 
8950 

8931 
8952 

8933 
8954 

•952 

8954 

8956 

8958 

8960 

8962 

8964 

8966 

8968 

8970 

8972 

8974 

•953 

8974 

8976 

8978 

8980 

8983 

8985 

8987 

8989 

8991 

8993 

8995 

•954 

8995 

8997 

8999 

9001 

9003 

9005 

9007 

9009 

9012 

9014 

9016 

.955 

9016 

9018 

9020 

9022 

9024 

9026 

9028 

9030 

9032 

9034 

9036 

•956 

9036 

9°39 

9041 

9043 

9045 

9047 

9049 

9051 

9053 

9055 

9057 

•957 

9057 

9°59 

9061 

9064 

9066 

9068 

9070 

9072 

9074 

9076 

9078 

•958 

9078 

9080 

9082 

9084 

9087 

9089 

9091 

9°93 

9095 

9097 

9099 

•959 

9099 

9101 

9103 

9J°5 

9108 

9110 

9112 

9114 

9116 

9118 

9120 

.960 

9120 

9122 

9124 

9126 

9129 

9i3i 

9133 

9135 

9U7 

9J39 

9141 

.961 

9141 

9H3 

9M5 

9H7 

9r5° 

9152 

9!54 

9*56 

9158 

9160 

9162 

.962 

9162 

9164 

9166 

9169 

9171 

9*73 

917S 

9177 

9179 

9181 

9183 

•963 

9183 

9185 

9188 

9190 

9192 

9194 

9196 

9198 

9200 

9202 

9204 

.964 

9204 

9207 

9209 

9211 

9213 

9215 

9217 

9219 

9221 

9224 

9226 

.965 

9226 

9228 

9230 

9232 

9234 

9236 

9238 

9241 

9243 

9245 

9247 

.966 

9247 

9249 

9251 

9253 

9256 

9258 

9260 

9262 

9264 

9266 

9268 

•967 

9268 

9270 

9273 

9275 

9277 

9279 

9281 

9283 

9285 

9288 

9290 

.968 

9290 

9292 

9294 

9296 

9298 

9300 

9303 

9305 

93°7 

93°9 

9311 

.969 

9311 

9313 

9315 

93i8 

9320 

9322 

9324 

9326 

9328 

9330 

9333 

.970 

9333 

9335 

9337 

9339 

934i 

9343 

9345 

9348 

935° 

9352 

9354 

.971 

9354 

9356 

9358 

9361 

9363 

9365 

9367 

9369 

937i 

9373 

9376 

.972 

9376 

9378 

9380 

9382 

9384 

9386 

9389 

939i 

9393 

9395 

9397 

•973 

9397 

9399 

9402 

9404 

9406 

9408 

9410 

9412 

94i5 

94i7 

9419 

•974 

9419 

9421 

9423 

9425 

9428 

943° 

9432 

9434 

9436 

9438 

9441 

.975 

9441 

9443 

9445 

9447 

9449 

9451 

9454 

9456 

9458 

9460 

9462 

.976 

9462 

9465 

9467 

9469 

947i 

9473 

9475 

9478 

9480 

9482 

9484 

•977 

9484 

9486 

9489 

949  1 

9493 

9495 

9497 

9499 

9502 

9504 

9506 

.978 

9506 

9508 

9510 

95*3 

9515 

951? 

95J9 

952i 

9524 

9526 

9528 

•979 

9528 

953° 

9532 

9535 

9537 

9539 

954i 

9543 

9546 

9548 

9550 

980 

955° 

9552 

9554 

9557 

9559 

956i 

95g3 

9565 

9568 

9570 

9572 

.981 

9572 

9574 

9576 

9579 

95»i 

9583 

9585 

9587 

959° 

9592 

9594 

.982 

9594 

9598 

9601 

9603 

9605 

9607 

9609 

9612 

9614 

9616 

•983 

9616 

9618 

9621 

9623 

9625 

9627 

9629 

9632 

9634 

9636 

9638 

.984 

9638 

9641 

9643 

9645 

9647 

9649 

9652 

9654 

9656 

9658 

9661 

.985 

9661 

9663 

9665 

9667 

9669 

9672 

9674 

9676 

9678 

9681 

9683 

.986 

9683 

9685 

9687 

9689 

9692 

9694 

9696 

9698 

9701 

9703 

9705 

!  -987 

9705 

9707 

9710 

9712 

97  T4 

9716 

97  19 

9721 

9723 

9725 

9727 

.988 
.989 

9727 
9750 

9730 
9752 

9732 
9754 

9734 
9757 

9736 
9759 

9739 
9761 

974i 
9763 

9743 
9766 

9745 
9768 

9748 
9770 

975° 
9772 

.990 

9772 

9775 

9777 

9779 

9781 

9784 

9786 

9788 

9790 

9793 

9795 

•99  i 

9795 

9797 

9799 

9802 

9804 

9806 

9808 

9811 

9813 

9815 

9817 

.992 

9817 

9820 

9822 

9824 

9827 

9829 

9831 

9833 

9838 

9840 

•993 

9840 

9842 

9845 

9847 

9849 

9851 

9854 

9856 

9858 

9861 

9863 

•994 

9863 

9865 

9867 

9870 

9872 

9874 

9876 

9879 

9881 

9883 

9886 

.995 

9886 

9888 

9890 

9892 

9895 

9897 

9899 

9901 

9904 

9906 

9908 

.996 

9908 

9911 

9913 

9915 

9917 

9920 

9922 

9924 

9927 

9929 

993i 

•997 

993  i 

9933 

9936 

9938 

9940 

9943 

9945 

9947 

9949 

9952 

9954 

•998 

9954 

99  56 

9959 

9961 

9963 

9966 

996g 

9970 

9972 

9975 

9977 

•999 

9977 

9979 

9982 

9984 

9986 

9988 

999  i 

9993 

9995 

9998 

oooo 

SMITHSONIAN  TABLES. 


TABLE  11. 
CIRCULAR  (TRIGONOMETRIC)  FUNCTIONS. 

(Taken  from  B.  O.  Peirce's  "  Short  Table  of  Integrals,"  Ginn  &  Co.) 


1  . 

i  ™ 

SINES. 

COSINES. 

TANGENTS. 

COTANGENTS. 

§£ 

«W 

^ 

0 

Nat.    Log. 

Nat.    Log. 

Nat.    Log. 

Nat.     Log. 

o.oooo 

0°00' 

.OOOO    00 

I.  OOOO  O.OOOO 

.OOOO    00 

00        00 

9o°oo' 

1.5708 

0.0029 

10 

.0029  7.4637 

I.  OOOO   .OOOO 

.0029  7.4637 

343-77   2.5363 

5° 

0.0058 

20 

.0058  .7648 

I.  OOOO   .OOOO 

.0058  .7648 

171.89    .2352 

40 

1.565° 

0.0087 

3° 

.0087  .9408 

I.  OOOO   .OOOO 

.0087  .9409 

114.59    -0591 

3° 

1.5621 

0.0116 

40 

.0116  8.0658 

.9999  .0000 

.0116  8.0658 

85.940  1.9342 

20 

J«5592 

0.0145 

50 

.0145  .1627 

.9999  .0000 

.0145   .1627 

68.750   .8373 

10 

^5563 

0.0175 

I°00' 

.0175  8.2419 

.9998  9.9999 

.0175  8.2419 

57.290  1.7581 

S9°oo' 

1-5533 

0.0204 

IO 

.0204  .3088 

.9998  .9999 

.0204  .3089 

49.104   .6911 

5° 

1-5504 

0.0233 

20 

.0233  .3668 

•9997  -9999 

•0233  .3669 

42.964   .6331 

40 

!-5475 

0.0262 

30 

.0262  .4179 

•9997  -9999 

.0262  .4181 

38.188   .5819 

3° 

1.5446 

0.0291 

40 

.0291  .4637 

.9996  .9998 

.0291  .4638 

34.368   .5362 

20 

1  0.0320 

50 

.0320  .5050 

•9995  -9998 

•0320  .5053 

31.242   .4947 

IO 

1^5388 

0.0349 

2°00' 

.0349  8.5428 

•9994  9-9997 

•0349  8.5431 

28.636  1.4569 

88°oo' 

J-5359 

0.0378 

10 

-0378  .5776 

•9993  -9997 

•0378  .5779 

26.432   .4221 

5° 

I-533° 

0.0407 

20 

.0407  .6097 

.9992  .9996 

.0407  .6101 

24-542   .3899 

40 

0.0436 

3° 

.0436  .6397 

.9990  .9996 

.0437  .6401 

22.904   .3599 

3° 

1.5272 

0.0465 

40 

.0465  .6677 

•9989  -9995 

.0466  .6682 

21.470   .3318 

20 

1-5243 

0.0495 

50 

.0494  .6940 

.9988  .9995 

.0495  .6945 

20.206   .3055 

IO 

1-5213 

0.0524 

3°oo' 

.0523  8.7188 

.9986  9.9994 

.0524  8.7194 

19.081  1.2806 

87°oo' 

1.5184 

0-0553 

10 

.0552  .7423 

•9985  -9993 

•0553  -7429 

18.075   -2571 

5° 

I-5I55 

0.0582 

20 

.0581  .7645 

.9983  .9993 

.0582  .7652 

17.169   .2348 

40 

1.5126 

0.06  u 

3° 

.0610  .7857 

.9981  .9992 

.0612  .7865 

16.350   .2135 

3° 

I-5097 

0.0640 

40 

.0640  .8059 

-998o  .9991 

.0641  .8067 

15.605   .1933 

20 

1.5068 

0.0669 

5° 

.0669  .8251 

.9978  .9990 

.0670  .8261 

14.924   .1739 

IO 

T-5°39 

0.0698 

4°oo/ 

.0698  8.8436 

.9976  9.9989 

.0699  8.8446 

14.301  1.1554 

86°oo' 

1.5010 

0.0727 

IO 

.0727  .8613 

•9974  -9989 

.0729  .8624 

J3-727   .1376 

5° 

1.4981 

0.0756 

20 

.0756  .8783 

.9971   .9988 

•0758  .8795 

13.197   .1205 

40 

1.4952 

0.0785 

30 

.0785  .8946 

•9969  -9987 

.0787  .8960 

12.706   .1040 

30 

1.4923 

0.0814 

40 

.0814   .9104 

•9967   -9986 

.0816  .9118 

12.251   .0882 

20 

1.4893 

0.0844 

50 

.0843  .9256 

.9964  -9985 

.0846  .9272 

11.826   .0728 

10 

1.4864 

0.0873 

5°oo' 

•0872  8.9403 

.9962  9.9983 

.0875  8.9420 

11.430  1.0580 

85°oo' 

1.4835 

0.0902 

10 

•0901  .9545 

•9959  -9982 

.0904  .9563 

11.059   .0437 

50 

i  .4806 

0.0931 

20 

•0929  .9682 

•9957  -9981 

•0934  .9701 

10.712   .0299 

40 

1-4777 

0.0960 
0.0989 

3° 

40 

.0958  .9816 
•0987  -9945 

-9954  .9980 
•995  i   -9979 

.0963   .9836 

.0992  .9966 

10.385   .0164 
10.078   .0034 

30 

20 

1.4748 
1.4719 

0.1018 

50 

.1016  9.0070 

.9948  .9977 

.1022  9.0093 

9.7882  0.9907 

10 

1.4690 

0.1047 
0.1076 

6°oo 

10 

.1045  9.0192 
.1074  .0311 

•9945  9-9976 
•9942  .9975 

.IO5I  9.0216 
.I080   .0336 

9.5144  0.9784 
9.2553  .9664 

84°oo' 
50 

1.4661 
1.4632 

0.1105 

20 

.1103  .0426 

•9939  -9973 

.1110  .0453 

9.0098  .9547 

40 

1.4603 

0.1134 

30 

."32  .0539 

.9936  .9972 

.1139  .0567 

8.7769  .9433 

3° 

1-4574 

0.1164 

40 

.1161  .0648 

•9932  -997I 

.1169  .0678 

8-5555  -9322 

20 

1-4544 

0.1193 

50 

.1190  -.0755 

.9929  .9969 

.1198  .0786 

8.3450  .9214 

10 

I-45I5 

0.1222 

7°oo' 

.1219  9.0859 

.9925  9.9968 

.1228  9.0891 

8.1443  0.9109 

83°oo' 

1.4486 

O.I25I 
O.I28O 

10 

20 

.1248  .0961 
.1276  .1060 

.9922  .9966 
.9918  .9964 

•I257  .0995 
.1287  .1096 

7.9530  -9005 
7.7704  .8904 

50 
40 

1-4457 
1.4428 

0.1309 

30 

.13%  .1157 

.9914  .9963 

.1317   .1194 

7.5958  .8806 

3° 

1-4399 

0.1338 

40 

.1334  .1252 

.9911   .9961 

.1346  .1291 

7.4287  .8709 

20 

1.4370 

0.1367 

50 

•1363  -1345 

•9907  -9959 

•1376  .1385 

7.2687  .8615 

10 

I.434I 

0.1396 

8°oo' 

•1392  9-1436 

•9903  9-9958 

.1405  9.1478 

7.1154  0.8522 

82°00' 

1.4312 

0.1425 

IO 

.1421  .1525 

.9899  .9956 

-1435  ^569 

6.9682  .8431 

50 

1.4283 

0.1454 

20 

.1449  .1612 

•9894  -9954 

.1465  .1658 

6.8269  .8342 

40 

1.4254 

0.1484 

3° 

40 

.1478  .1697 
.1507  .1781 

.9890  .9952 
.9886  .9950 

•  1495  -T745 
.1524  .1831 

6.6912  .8255 
6.5606  .8169 

30 

20 

1.4224 

0.1542 

50 

.1536  .1863 

.9881   .9948 

.1554  .1915 

6.4348  .8085 

IO 

1.4166 

0.1571 

9°oo' 

.1564  9.1943 

.9877  9.9946 

.1584  9.1997 

6.3138  0.8003 

8i°oo' 

I.4I37 

Nat.   Log. 

Nat.    Log. 

Nat.    Log. 

Nat.      Log. 

c/5 

£ 

COSINES. 

SINES. 

COTAN- 
GENTS. 

TANGENTS. 

Qti 

O 

•j? 

SMITHSONIAN  TABLES. 


TABLE  1  1   (continued). 
CIRCULAR  (TRIGONOMETRIC)  FUNCTIONS. 


Sg 

C/3 

SINES. 

COSINES. 

TANGENTS. 

COTANGENTS. 

23 

0 

Nat.   Log. 

Nat.   Log. 

Nat.   Log. 

Nat.    Log. 

0.1571 

9°oo/ 

.1564  9.1943 

.9877  9.9946 

.1584  9.1997 

6.3138  0.8003 

8i°oo/ 

1.4137 

0.1600 

IO 

.1593   .2022 

.9872   .9944 

.1614   .2078 

6.1970   .7922 

5° 

1.4108 

0.1629 

20 

.1622   .2100 

.9868   .9942 

.1644   .2158 

6.0844   .7842 

40 

1.4079 

0.1658 
0.1687 

30 
40 

.1650  .2176 
.1679  -2251 

.9863   .9940 
•985»   .9938 

.1673   -2236 
.1703   .2313 

5.9758   .7764 
5.8708   .7687 

30 

20 

1.4050 
1.4021 

0.1716 

50 

.1708  .2324 

•9853   ^936 

.1733   -2389 

5.7694   .7611 

10 

1.3992 

0.1745 

I0°00' 

.1736  9-2397 

.9848  9.9934 

.1763  9.2463 

5.6713  0.7537 

8o°oo' 

J-3963 

0.1774 

IO 

.1765  .2468 

•9843   -993  i 

.1793   -2536 

5-5764   .7464 

50 

J-3934 

0.1804 

20 

.1794  .2538 

.9838   .9929 

.1823   .2609 

5.4845   .7391 

40 

1.3904 

0.1833 

30 

.1822  .2606 

•9833   -9927 

.1853   .2680 

5-3955  -7320 

30 

I-3875 

0.1862 

40 

.1851  .2674 

.9827   .9924 

.1883   .2750 

5-3093  -7250 

20 

1.3846 

0.1891 

5° 

.1880  .2740 

.9822   .9922 

.1914   .2819 

5.2257  .7181 

IO 

1.3817 

0.1920 

1  I°00' 

.1908  9.2806 

.9816  9.9919 

.1944  9.2887 

5.1446  0.7113 

79°oo' 

1.3788 

0.1949 

10 

.1937  .2870 

.9811   .9917 

•1974   .2953 

5.0658  .7047 

50 

1-3759 

0.1978 

20 

.1965  .2934 

.9805   .9914 

.2004   .3020 

4.9894  .6980 

40 

1-3730 

0.2007 

3°. 

.1994  .2997 

•9799  -99  J  2 

•2035   -3085 

4.9152  .6915 

3° 

1.3701 

0.2036 

40 

.2022   .3058 

•9793  -9909 

.2065   .3149 

4.8430  .68  c  i 

20 

1.3672 

0.2065 

50 

.2051   .3119 

.9787  .9907 

.2095   -3212 

4.7729  .6788 

10 

1-3643 

0.2094 

I2°00/ 

.2079  9.3179 

.9781  9.9904 

.2126  9.3275 

4.7046  0.6725 

78°oo' 

1.3614 

0.2123 

10 

.2108   .3238 

•9775  -9901 

.2156   .3336 

4.6382  .6664 

5° 

1-3584 

0-2153 

20 

.2136   .3296 

.9769  .9899 

.2186   .3397 

4.5736  .6603 

40 

J-3555 

0.2182 

3° 

•2164   -3353 

.9763  .9896 

•2217   .3458 

4.5107  .6542 

30 

1-3526 

0.221  1 

40 

.2193   .3410 

•9757  .9893 

-2247  .35J7 

4.4494  .6483 

20 

O.224O 

50 

.2221   .3466 

.9750  .9890 

.2278  .3576 

4.3897  .6424 

IO 

1^3468 

O.2269 

13000' 

.2250  9.3521 

.9744  9.9887 

.2309  9.3634 

4.3315  0.6366 

77°oo' 

J-3439 

0.2298 

IO 

•2278.   .3575 

•9737   -9884 

•2339  .3691 

4.2747  .6309 

5° 

1.3410 

0.2327 

20 

.2306   .3629 

.9730  .9881 

.2370  .3748 

4.2193  .6252 

40 

0.2356 

30 

.2334   .3682 

.9724  .9878 

.2401  .3804 

4.1653  .6196 

3° 

J-3352 

0.2385 

40 

-2363  -3734 

•9717   -9875 

.2432  .3859 

4.1126  .6141 

20 

J-3323 

0.2414 

5° 

•2391  -3786 

.9710  .9872 

.2462  .3914 

4.0611  .6086 

IO 

i-3294 

0.2443 

i4°oo' 

.2419  9.3837 

•97°3  9-9869 

.2493  9.3968 

4.0108  0.6032 

76°oo' 

1-3265 

0.2473 

10 

.2447  .3887 

.9696  .9866 

.2524  .4021 

3-96i7  -5979 

50 

1.3235 

O.25O2 

20 

-2476  -3937 

.9689   .9863 

.2555  .4074 

3.9136  .5926 

40 

1.3206 

0.2531 

30 

.2504  .3986 

.9681   .9859 

.2586  .4127 

3.8667  .5873 

3° 

1.3177 

0.2560 
0.2589 

40 
50 

.2532  .4035 
.2560  .4083 

.9674   .9856 
.9667   .9853 

.2617  .4178 
.2648  .4230 

3.8208  .5822 
3.7760  .5770 

20 

10 

1.3148 
1.3119 

0.26l8 

i5°oo> 

.2588  9.4130 

.9659  9-9849 

.2679  9.4281 

3.7321  0.5719 

75°oo' 

1.3090 

0.2647 

10 

.2616  .4177 

.9652   .9846 

.2711  .4331 

3.6891   .5669 

5° 

1.3061 

0.2676 

20 

.2644  4223 

.9644  .9843 

.2742  .4381 

3.6470  .5619 

40 

1.3032 

0.2705 

30 

.2672  .4269 

.9636  .9839 

•2773  -443° 

3-6059  -5570 

30 

1-3003 

0.2734 

40 

.2700  .4314 

.9628  .9836 

.2805  .4479 

3.5656  .5521 

20 

1.2974 

0.2763 

50 

.2728  .4359 

.9621   .9832 

.2836  .4527 

3.5261  .5473 

10 

1.2945 

0.2793 

i6°oo' 

.2756  9.4403 

.9613  9.9828 

.2867  94575 

3.4874  0.5425 

74°oo' 

1.2915 

O.2822 

IO 

.2784  .4447 

.9605  .9825 

.2899  .4622 

3-4495  -5378 

50 

1.2886 

0.2851 

20 

.2812  .4491 

.9596  .9821 

.2931   .4669 

3.4124  .5331 

40 

1.2857 

0.2880 

30 

.2840  .4533 

.9588  .9817 

.2962  .4716 

3-3759  -5284 

30 

1.2828 

0.2909 

40 

.2868  .4576 

.9580  .9814 

.2994  .4762 

3.3402  .5238 

20 

1.2799 

0.2938 

5° 

.2896  .4618 

.9572  .9810 

.3026  .4808 

3.3052  .5192 

IO 

1.2770 

0.2967 
0.2996 

i7°oo' 

10 

.2924  9.4659 
.2952  .4700 

•9563  9-98o6 
•9555  -9802 

.3057  9-4853 
.3089  .4898 

3.2709  0.5147 
3.2371  .5102 

73°oo/ 
50 

1.2741 
1.2712 

0.3025 

20 

.2979  .4741 

•9546  .9798 

.3121   .4943 

3.2041   .5057 

40 

1.2683 

0.3054 

3° 

.3007  .4781 

•9537  .9794 

•3  '53  -4987 

3.1716  .5013 

30 

1.2654 

0.3083 

40 

.3035  .4821 

.9528  .9790 

•3185  .5031 

3.1397  .4969 

20 

1.2625 

0.3H3 

50 

.3062  .4861 

.9520  .9786 

•3217  .5075 

3.1084  .4925 

IO 

1-2595 

0.3142 

i8°oo' 

.3090  9.4900 

.9511  9.9782 

.3249  9.5118 

3.0777  0.4882 

72°00' 

1.2566 

Nat.   Log. 

Nat.   Log. 

Nat.   Log. 

Nat.    Log. 

Jj 

QC/5 

COSINES. 

SINES. 

COTAN- 
GENTS. 

TANGENTS 

o 

t< 

SMITHSONIAN  TABLES. 


TABLE    1  1  (continued). 
CIRCULAR  (TRIGONOMETRIC)  FUNCTIONS.. 


& 

$ 

ww 

SINES. 

COSINES. 

TANGENTS. 

COTANGENTS. 

x< 

Get 
o 

Nat.   Log. 

Nat.   Log. 

Nat.   Log. 

Nat.    Log. 

0.3142 

i8°oo' 

.3090  9.4900 

.9511  9.9782 

.3249  9.5118 

3.0777  0.4882 

72°00' 

.2566 

0.3171 

10 

.3118   .4939 

.9502   .9778 

.3281   .5161 

3.0475   .4839 

5° 

•2537 

0.3200 

20 

.3145   .4977 

•9492   -9774 

•3314   .5203 

3.0178   .4797 

40 

.2508 

0.3229 

3° 

•3J73  -5OI5 

.9483   .9770 

•3346   .5245 

2.9887   .4755 

30 

.2479 

0.3258 

40 

.3201  .5052 

•9474   -9765 

•3378   .5287 

2.9600   .4713 

2O 

•2450 

0.3287 

5° 

.3228  .5090 

•9465   .9761 

•3411   .5329 

2.9319   .4671 

10 

.2421 

0.3316 

i9°oo' 

.3256  9.5126 

•9455  9-9757 

•3443  9-5370 

2.9042  0.4630 

7i°oo/ 

.2392 

0-3345 

10 

•3283  -5163 

.9446  .9752 

•3476  .5411 

2.8770   .4589 

5° 

.2363 

0-3374 

20 

•33"  -5199 

.9436  .9748 

.3508  .5451 

2.8502   .4549 

40 

•2334 

0.3403 

30 

•3338  .5235 

.9426  .9743 

•3541  -5491 

2.8239   .4509 

30 

•2305 

0-3432 

40 

.3365  -5270 

•9417  -9739 

•3574  -5531 

2.7980   .4469 

20 

.2275 

0.3462 

50 

•3393  -5306 

.9407  .9734 

•3607  -557I 

2.7725   .4429 

IO 

.2246 

0.3491 

20°00' 

.3420  9.5341 

•9397  9-9730 

.3640  9.5611 

2.7475  04389 

7o°oo' 

.2217 

0.3520 

IO 

•3448  .5375 

•9387  -9725 

•3673  -5650 

2.7228   .4350 

59 

.2188 

Q-3549 

20 

-3475  -5409 

•9377  -9721 

.3706  .5689 

2.6985   .4311 

40 

.2159 

0.3578 

30 

.3502  .5443 

.9367  .9716 

•3739  -5727 

2.6746   .4273 

30 

.2130 

0.3607 

40 

.3529  -5477 

.9356  .9711 

.3772  .5766 

2.6511   .4234 

20 

.2IOI 

0.3636 

56 

•3557  .55*0 

•934$  -9706 

.3805  .5804 

2.6279   .4196 

IO 

.2072 

0.3665 

2I°00' 

•3584  9-5543 

.9336  9.9702 

•3839  9-5842 

2.6051  0.4158 

69°oo' 

.2043 

0.3694 

IO 

•3611  -5576 

•9325  -9697 

.3872  .5879 

2.5826   .4121 

5° 

.2014 

0.3723 

20 

.3638  .5609 

.9315  .9692 

.3906  .5917 

2.5605   .4083 

40 

.1985 

0.3752 

30 

.3665  .5641 

.9304  .9687 

•3939  -5954 

2.5386   .4046 

30 

.1956 

0.3782 

40 

.3692  .5673 

.9293  .9682 

•3973  .5991 

2.5172   .4009 

20 

.1926 

0.3811 

50 

.3719  .5704 

.9283  .9677 

.4006  .6028 

2.4960   .3972 

IO 

.1897 

0.3840 

22°OO' 

.3746  9-5736 

.9272  9.9672 

.4040  9.6064 

2.4751  0.3936 

68°oo' 

.1868 

0.3869 

10 

•3773  -5767 

.9261   .9667 

.4074  .6100 

2-4545  -3900 

5° 

.1839 

0.3898 

20 

.3800  .5798 

.9250  .9661 

.4108  .6136 

2.4342  .3864 

40 

.1810 

0.3927 

3° 

.3827   .5828 

.9239  -9656 

.4142  .6172 

2.4142  .3828 

30 

.1781 

0.3956 

40 

.3854  -5859 

.9228  .9651 

.4176  .6208 

2-3945  -3792 

20 

•1752 

0.39^5 

50 

.3881   .5889 

.9216  .9646 

.4210  .6243 

2.3750  -3757 

IO 

•1723 

0.4014 

23°00' 

.3907  9-59!9 

.9205  9.9640 

.4245  9.6279 

2-3559  0.3721 

67°oo' 

.1694 

0.4043 

10 

•3934  .5948 

.9194  .9635 

.4279  .6314 

2.3369  -3686 

50 

.1665 

0.4072 
0.4102 

20 
3° 

.3961  .5978 
.3987  .6007 

.9182  .9629 
.9171   .9624 

.4314  .6348 
.4348  .6383 

2.3183  .3652 
2.2998  .3617 

40 
30 

.1636 
.1606 

0.4131 
0.4160 

40 
50 

.4014  .6036 
.4041  .6065 

.9159  .9618 
.9147   .9613 

.4383  .6417 
.4417   .6452 

2.2817  .3583 
2-2637  .3548 

20 
IO 

.1577 
.1548 

0.4189 

24°00' 

.4067^  9.6093 

•9135  9-96o7 

.4452  9.6486 

2.2460  0.3514 

66°oo' 

-1S19 

0.4218 

10 

.4094  .6121 

.9124  .9602 

.4487   .6520 

2.2286  .3480 

5° 

.1490 

0.4247 

20 

.4120  .6149 

.9112  .9596 

.4522  .6553 

2.2113  .3447 

40 

.1461 

0.4276 

3° 

.4147  .6177 

.9100  .9590 

.4557  .6587 

2.1943  .3413 

30 

.1432 

0-4305 
0.4334 

40 
50 

.4173  .6205 
.4200  .6232 

.9088  .9584 
•9075  -9579 

.4592  .6620 
.4628  .6654 

2-1775  -3380 
2.1609  .3346 

20 
10 

.1403 
•1374 

o-4363 

25°00' 

.4226  9.6259 

•9063  9-9573 

.4663  9.6687 

2.1445  o-33T3 

65°oo' 

•1345 

0.4392 

IO 

.4253  .6286 

.9051   .9567 

.4699  .6720 

2.1283  .3280 

50 

•'316 

0.4422 

20 

.4279  .6313 

.9038  .9561 

•4734  -6752 

2.1123  .3248 

40 

.1286 

0.4451 

30 

•43°5  -6340 

.9026  .9555 

.4770  .6785 

2.0965  .3215 

3° 

•1257 

0.4480 

40 

.4331   .6366 

.9013  .9549 

.4806  .6817 

2.0809  -3l83 

20 

.1228 

0.4509 

50 

.4358  .6392 

.9001  .9543 

.4841   .6850 

2.0655  -3150 

10 

.1199 

0.4538 

26°00' 

.4384  9.6418 

•8988  9-9537 

.4877  9.6882 

2.0503  0.3118 

64°oo' 

.1170 

0.4567 

IO 

.4410  .6444 

•8975  -953° 

.4913  .6914 

2-0353  -3086 

50 

.1141 

0.4596 

20 

.4436  .6470 

.8962  .9524 

.4950  .6946 

2.0204  -3°54 

40 

.1112 

0.4625 

30 

.4462  .6495 

.8949  .9518 

.4986  .6977 

2.0057  .3023 

3° 

.1083 

0.4654 

40 

.4488  .6521 

.8936  .9512 

.5022   .7009 

1.9912  .2991 

20 

.1054 

0.4683 

50 

.4514  .6546 

•8923  -95°5 

•5059  .7040 

1.9768  .2960 

IO 

.'1025 

0.4712 

27°00' 

.4540  9.6570 

.8910  9.9499 

.5095  9.7072 

1.9626  0.2928 

63°oo' 

1.0996 

Nat.   Log. 

Nat.   Log. 

Nat.   Log. 

Nat.    Log. 

CO 

'  w 

i 

Q^" 

COSINES. 

SINES. 

COTAN- 
GENTS. 

TANGENTS. 

WM 

o2 

o 

g 

SMITHSONIAN  TABLES. 


TABLE  1  1   (continued). 
CIRCULAR  (TRIGONOMETRIC)  FUNCTIONS. 


33 


¥ 

& 

SINES. 

COSINES. 

TANGENTS. 

COTANGENTS. 

K* 

Qp< 
O 

Nat.   Log. 

Nat.   Log. 

Nat.   Log. 

Nat.    Log. 

0.4712 

27°00' 

.4540  9.6570 

.8910  9.9499 

.5095  9.7072 

1.9626  0.2928 

63°00' 

1.0996 

0.4741 

10 

.4566   .6595 

.8897   .9492 

.5132   .7103 

1.9486   .2897 

50 

1.0966 

0.4771 

20 

.4592   .6620 

.8884   .9486 

.5169   .7134 

1.9347   .2866 

40 

I-°937 

0.4800 

30 

.4617   .6644 

.8870   .9479 

.5206   .7165 

1.9210   .2835 

3° 

0.4829 
0.4858 

40 
50 

.4643  .6668 
.4669  .6692 

•885?   -9473 
.8843   .9466 

.5243   .7196 
.5280   .7226 

1.9074   .2804 
1.8940   .2774 

2O 
10 

1.0879 
1.0850 

0.4887 

28°00' 

.4695  9.6716 

•8829  9.9459 

•5317  9.7257 

1.8807  °-2743 

62°00' 

1.0821 

0.4916 

10 

.4720  .6740 

.8816.  .9453 

-5354  -7287 

1.8676   .2713 

5° 

1.0792 

0.4945 

20 

.4746  .6763 

.8802   .9446 

•5j92  -73  i  7 

1.8546   .2683 

40 

1.0763 

0.4974 

30 

.4772  .6787 

.8788   .9439 

.5430  .7348 

1.8418   .2652 

3° 

1-0734 

0.5003 

40 

.4797  .6810 

.8774   .9432 

-5467  .7378 

1.8291   .2622 

20 

1.0705 

0.5032 

50 

.4823  .6833 

.8760   .9425 

.5505  .7408 

1.8165   .2592 

10 

1.0676 

0.5061 

29°00' 

.4848  9.6856 

.8746  9.9418 

§3  9-7438 

1.8040  0.2562 

6i°oo' 

1.0647 

0.5091 

10 

.4874  .6878 

.8732   .9411 

i   .7467 

I-79I7   .2533, 

5° 

1.0617 

0.5120 

20 

.4899  .6901 

.8718   .9404 

9  -7497 

1.7796   .2503 

40 

1.0588 

0.5149 

3° 

.492^  .6923 

•8704  -9397 

.5658  .7526 

1.7675   .2474 

30 

I-°559 

0.5178 

40 

.4950  .6946 

.8689  .9390 

-5696  .7556 

1.7556   .2444 

20 

1.0530 

0.5207 

50 

•4975  -6968 

•8675  -9383 

-5735  7585 

1.7437  ,  .2415 

10 

1.0501 

0.5236 

3o°oo' 

.5000  9.6990 

.8660  9.9373 

•5774  9-76i4 

I.7J&I  0.2386 

6o°oo' 

1.0472 

0.5265 

10 

.5025  .7012 

.8646  .9368 

.5812  .7644 

1.7205  .2356 

5° 

1.0443 

0.5294 

20 

•5050  -7033 

•8631   .9361 

•5851   -7673 

1.7090  .2327 

40 

1.0414 

0-5323 

30 

•5°75  -7055 

•8616  .9353 

.5890  .7701 

1.6977.  -2299 

30 

1.0385 

0-5352 

40 

.5100  .7076 

.8601   .9346 

•5930  -7730 

1.6864  .2270 

20 

1.0356 

0.5381 

50 

.5125  .7097 

•8587  .9338 

•5969  -7759 

1.6753   -2241 

IO 

1.0327 

0.5411 

3I°00' 

.5150  9.7118 

•8572  9-9331 

.6009  9.7788 

1.6643  O.22I2 

59°oo' 

1.0297 

0.5440 

10 

•5'75  -7139 

•8557  .9323 

.6048  .7816 

1.6534   .2184 

5° 

1.0268 

0.5469 

20 

.5200  .7160 

•8542  .93'5 

.6088  .7845 

1.6426   .2155 

40 

1.0239 

0.5498 

3° 

.5225  .7181 

.8526  .9308 

.6128  .7873 

1.6319   .2127 

30 

1.  02  10 

0-5527 

40 

.5250  .7201 

.8511   .9300 

.6168  .7902 

I.62I2   .2098 

20 

I.OlSl 

0.5556 

50 

.5275  .7222 

.8496  .9292 

.6208  .7930 

I.6lO7   .2O7O 

10 

I.OI52 

0-5585 

32°00' 

.5299  9.7242 

.8480  9.9284 

•6249  9-7958 

1.6003  O.2O42 

58°oo' 

I.OI23 

0.5614 

IO 

.5324  .7262 

.8465  .9276 

.6289  .7986 

1.5900   .2014 

5° 

1.0094 

0.5643 

20 

.5348  .7282 

.8450  .9268 

.6330  .8014 

1.5798   .1986 

40 

1.0065 

0.5672 

3° 

•5373  -7302 

.8434  .9260 

.637  i   .8042 

1.5697   .1958 

3° 

1.0036 

0.5701 

40 

.5398  .7322 

.8418  .9252 

.6412  .8070 

'•5597  -193° 

20 

I.OOO7 

0.5730 

5° 

.5422  .7342 

.8403  .9244 

.6453  .8097 

1.5497  .1903 

IO 

0.9977 

0.5760 

33000' 

•5446  9-736i 

-8387  9-9236 

.6494  9.8125 

1-5399  0.1875 

57°oo' 

0.9948 

0.5789 

IO 

•5471   -738° 

.8371   .9228 

•6536  .8153 

1.5301  .1847 

50 

0.9919 

0.5818 

20 

•5495  -7400 

.8355  .9219 

.657^  .8180 

1.5204  .1820 

40 

0.9890 

0.5847 

3° 

•55*9  -7419 

.8339  .9211 

.6619  .8208 

1.5108  .1792 

3° 

0.9861 

0.5876 
0-5905 

40 
50 

•5544  -743s 
.5568  .7457 

-8323  -9203 
.8307   .9194 

.6661   .8235 
.6703  .8263 

1.5013  .1765 
1.4919  .1737 

20 

10 

0.9832 
0.9803 

0-5934 

34°oo' 

•5592  9-7476 

.8290  9.9186 

.6745  9.8290 

1.4826  0.1710 

56°oo' 

0.9774 

0-5963 

IO 

.5616  .7494 

.8274  .9177 

.6787  .8317 

1.4733  -l683 

5° 

0-9745 

0.5992 

20 

.5640  .7513 

.8258  .9169 

.6830  .8344 

1.4641  .1656 

40 

0.9716 

0.6021 

3° 

.5664  .7531 

.8241   .9160 

.6873  .8371 

1.4550  .1629 

30 

0.9687 

0.6050 

40 

.5688  .7550 

.8225   .9151 

.6916  .8398 

1.4460  .1602 

20 

0.9657 

0.6080 

5° 

.5712  .7568 

.8208  .9142 

.6959  .8425 

1.4370  .1575 

10 

0.9628 

0.6109 

35<>oo' 

.5736  9.7586 

.8192  9.9134 

.7d02  9.8452 

1.4281  0.1548 

55°oo' 

0.9599 

0.6138 
0.6167 

10- 
20 

.5783  .7622 

•8i7S  -9125 
.8158  .9116 

.7046  .8479 
.7089  .8506 

1.4193  .1521 
1.4106  .1494 

50 
40 

0.9570 
0.9541 

0.6196 

3° 

.5807  .7640 

.8141   .9107 

•7133  -8533 

1.4019  .1467 

30 

0.9512 

0.6225 

40 

.5831   .7657 

.8124  .9098 

•7i77  -8559 

1.3934  .1441 

20 

0.9483 

0.6254 

50 

.5854  .7675 

.8107  .9089 

.7221  .8586 

1.3848  .1414 

IO 

0.9454 

0.6283 

36°oo' 

.5878  9.7692 

.8090  9.9080 

.7265  9.8613 

1.3764  0.1387 

54°oo' 

0.9425 

Nat.   Log. 

Nat.   Log. 

Nat.   Log. 

Nat.    Log. 

OT 

AW 

t 

5</5 

COSINES. 

SINES. 

COTAN- 
GENTS. 

TANGENTS. 

a  W 

Qa 

o 

£ 

SMITHSONIAN  TABLES. 


34 


TABLE  1  1  (continued). 
CIRCULAR  (TRIGONOMETRIC)  FUNCTIONS, 


§* 

c/5 
\M 

Wy 

SINES. 

COSINES. 

TANGENTS. 

COTANGENTS 

«< 

Qp4 

o 

Nat.   Log. 

Nat.   Log. 

Nat.   Log. 

Nat.    Log. 

0.6283 

36°oo' 

.5878  9.7692 

.8090  9.9080 

.7265  9.8613 

1.3764  0.1387 

54°00' 

0.9425 

0.6312 

10 

.5901   .7710 

.8073   .9070 

.7310   .8639 

1.3680   .1361 

50 

0.9396 

0.6341 

20 

.5925   .7727 

.8056   .9061 

.7355   -8666 

J-3597   -1334 

40 

0.9367 

0.6370 

3° 

.5948   .7744 

•8039   .9052 

.7400   .8692 

1.3514   .1308 

3° 

0-9338 

0.6400 

40 

.5972   .7761 

.8021   .9042 

•7445   -8718 

1.3432   .1282 

20 

0.9308 

0.6429 

5° 

•5995  -7778 

.8004   .9033 

.7490  .8745 

1.3351   .1255 

IO 

0.9279 

0.6458 

37°oo' 

•6018  9.7795 

.7986  9.9023 

•7536  9-877I 

1.3270  0.1229 

53°oo' 

0.9250 

0.6487 

10 

.6041  .7811 

.7969   .9014 

.7581   ,8797 

1.3190   .1203 

5° 

0.9221 

0.6516 

20 

.6065  .7828 

•795  l   -9004 

.7627   .8824 

1.3111   .1176 

40 

0.9192 

0.6545 

30 

.6088  .7844 

•7934  -8995 

.7673   .8850 

1.3032   .1150 

30 

0.9163 

0.6574 
0.6603 

40 

50 

.6m  .7861 
.6134  -7877 

.7916  .8985 
.7898  .8975 

.7720   .8876 
.7766  .8902 

1.2954   .1124 
1.2876   .1098 

20 
IO 

0.9134 
0.9105 

0.6632 

38°oo' 

•6157  97893 

.7880  9.8965 

.7813  9.8928 

1.2799  0.1072 

52°00' 

0.9076 

0.6661 

10 

.6180  .7910 

.7862  .8955 

.7860  .8954 

1.2723   .1046 

5° 

0.9047 

0.6690 

20 

.6202  .7926 

.7844  .8945 

.7907   .8980 

1.2647   •102<^> 

40 

0.9018 

0.6720 

3° 

.6225  .7941 

•7826  .8935 

•7954  •9°°6 

1.2572  ^994 

3° 

0.8988 

0.6749 

40 

.6248  .7957 

.7808  .8925 

.8002  .9032 

1.2497  70968 

20 

0.8959 

0.6778 

50 

.6271  .7973 

.7790  .8915 

.8050  .9058 

1.2423  .0942 

10 

0.8930 

0.6807 

39°oo' 

.6293  9.7969 

.7771  9.8905 

.8098  9.9084 

1.2349  0.0916 

5i°oo' 

0.8901 

0.6836 

10 

.6316  .8004 

7753  -8895 

.8146  .9110 

1.2276  .0890 

50 

0.8872 

0.6865 

20 

.6338  .8020 

-7735  -8884 

•8i95  -9!35 

1.2203  .0865 

40 

0.8843 

0.6894 

3° 

.6361  .8035 

.7716  .8874 

.8243  .9161 

1.2131   .0839 

3° 

0.8814 

0.6923 
0.6952 

40 
50 

.6383  .8050 
.6406  .8066 

.7698  .8864 
.7679  .8853 

.8292  .9187 
.8342  .9212 

1.2059  .0813 
1.1988  .0788 

20 

10 

0.8785 
0.8756 

0.6981 

40°oo' 

.6428  9.8081 

.7660  9.8843 

•8391  9-9238 

1.1918  0.0762 

5o°oo' 

0.8727 

0.7010 

IO 

.6450  .8096 

.7642  .8832 

.8441   .9264 

1.1847  -0736 

5° 

0.8698 

0.7039 

20 

.6472  .8m 

.7623  .8821 

.8491   .9289 

1.1778  .0711 

40 

0.8668 

30 

.6494  .8125 

.7604  .8810 

•8541   .93r5 

1.1708  .0685 

30 

0.8639 

0.7127 

40 
50 

.6517  .8140 
•6539  -8155 

.7585  .8800 
.7566  .8789 

•8591   -934I 
.8642  .9366 

1.1640  .0659 
1.1571   .0634 

20 
10 

0.8610 
0.8581 

0.7156 

4i°oo' 

.6561  9.8169 

•7547  9-8778 

•8693  9-9392 

1.1504*0.0608 

49°oo' 

0.8552 

0.7185 

10 

.6583  .8184 

.7528  .8767 

.8744  .9417 

1.1436  .0583 

50 

0.8523 

0.7214 

20 

.6604  .8198 

•7509  -8756 

.8796  .9443 

1.1369  .0557 

40 

0.8494 

0.7243 

3° 

.6626  .8213 

.7490  .8745 

.8847  .9468 

1-1303  -0532 

30 

0.8465 

0.7272 

40 

.6648  .8227 

.7470  .8733 

.8899  .9494 

1.1237   .0506 

20 

0.8436 

0.7301 

50 

.6670  .8241 

.7451   .8722 

.8952  .9519 

1.1171   .0481 

IO 

0.8407 

0-733° 

42°00' 

.6691  9.8255 

.7431  9.8711 

.9004  9.9544 

1.1106  0.0456 

48°oo' 

0.8378 

0-7359 

10 

.6713  .8269 

.7412  .8699 

•9°57  -9570 

1.1041  .0430 

5° 

0.8348 

0.7389 

20 

.6734  .8283 

.7392  .8688 

.9110  .9595 

1.0977  .0405 

40 

0.8319 

0.7418 

30 

.6756  .8297 

•7373  -8676 

.9163  .9621 

1.0913  .0379 

30 

0.8290 

0.7447 

40 

.6777  .8311 

•7353  -8665 

.9217  .9646 

1.0850  .0354 

20 

0.8261 

0.7476 

5° 

.6799  -8324 

•7333  -8653 

.9271   .9671 

1.0786  .0329 

10 

0.8232 

0-7505 

43°oo' 

.6820  9.8338 

.7314  9.8641 

•9325  9-9697 

1.0724  0.0303 

47°oo' 

0.8203 

0-7534 

10 

.6841  .8351 

.7294  .8629 

.9380  .9722 

1.0661   .0278 

50 

0.8174 

0.7563 

20 

.6862  .8365 

.7274  .8618 

•9435   -9747 

1.0599  .0253 

40 

0.8145 

0.7592 

30 

.6884  .8378 

.7254  .8606 

-949°  -9772 

1.0538  .0228 

30 

0.8116  | 

0.7621 

40 

.6905  .8391 

.7234  .8594 

•9545  -9798 

1.0477  .0202 

20 

0.8087 

0.7650 

50 

.6926  .8405 

.7214  .8582 

.9601   .9823 

1.0416  .0177 

10 

0.8058 

0.7679 

44°oo' 

.6947  9.8418 

.7193  9.8569 

.9657  9-9848 

1.0355  0.0152 

46°oo' 

0.8029 

0.7709 

IO 

.6967  .8431 

.7173  .8557 

.9713  .9874 

1.0295  .0126 

50 

0.7999 

0.7738 

20 

.6988  .8444 

•7153  -8545 

•9770  .9899 

1.0235  .0101 

40 

0.7970 

0.7767 
0.7796 

30 
40 

.7009  .8457 
.7030  .8469 

•7133  -8532 
.7112  .8520 

.9827  .9924 
.9884  .9949 

1.0176  .0076 
1.0117  .0051 

3° 

20 

0.7941 
0.7912 

0.7825 

50 

.7050  .8482 

.7092  .8507 

•9942  -9975 

1.0058  .0025 

IO 

0.7883 

0.7854 

45°oo' 

.7071  9.8495 

.7071  9.8495 

I.OOOO  O.OOOO 

I.OOOO  O.OOOO 

45°oo' 

0.7854 

Nat.   Log. 

Nat    Log. 

Nat.   Log. 

Nat.    Log. 

'  W 

5* 

COSINES. 

SINES. 

COTAN- 
GENTS. 

TANGENTS. 

W  y 

a* 
o 

<* 

(4** 

SMITHSONIAN  TABLES. 


TABLE  1 2. 
CIRCULAR  (TRIGONOMETRIC)  FUNCTIONS.* 


35 


RADIANS. 

SINES. 

COSINES. 

TANGENTS. 

COTANGENTS. 

DEGREES. 

Nat     Log. 

Nat.     Log. 

Nat.      Log. 

Nat.      Log. 

0.00 

.01 
.02 

.03 
.04 

O.OOOOO    —  00 

.01000  7-99999 
.02000  8.30100 
.03000   .47706 
.03999   -60194 

1.  00000   0.00000 

0-99995  9.99998 
.99980   .99991 
•99955   -99980 
.99920   .99965 

—  oo     —  oo 
o.oiooo  8.OOOOI 
.02000   .30109 

.03001  .47725 

.04002   .60229 

.00          00 

99-997   1-99999 
49.993    .69891 

33-323    .52275 
24.987    .39771 

00°00' 

0034 

oi  09 
oi  43 
02  18 

°s 

.07 
.08 
.09 

0.04998  8.69879 

•05996   .77789 
.06994   .84474 
.07991   .90263 
.08988   .95366 

0-99875  9-99946 
.99820   .99922 

•99755   -99894 
.99680   .99861 

•99595   -99824 

0.05004  8.69933 

.06007   -77867 
.07011   .84581 
.08017   .90402 

.09024  .95542 

J9-983   1.30067 
16.647    .22133 
14.262    .15419 
12473    -09598 
11.081    .04458 

02°52' 

03  26 
04  oi 

0435 
0509 

O.IO 

.11 

.12 

•13 
.14 

0.09983  8.99928 
.10978  9.04052 
.11971   .07814 
.12963   .11*72 
.13954   .14471 

0.99500  9.99782 
.99396   .99737 
.99281   .99687 
.99156   .99632 
•99022   .99573 

0.10033  9.00145 

.11045   -043I5 
.12058   .08127 
.13074   .11640 
.14092   .14898 

9.9666  0.99855 
9.0542   .95685 
8.2933   -91873 
7.6489   .88360 
7.0961   .85102 

Sl°4f 

06  18 

0653 
07  27 
0801 

o-'S 

.16 

•17 
.18 
.19 

0.14944  9-  *  7446 
.15932   .20227 
.16918   .22836 

!i8886   .27614 

0.98877  9.99510 
.98723   .99442 
.98558   .99369 
.98384   .99293 
.98200   .99211 

0.15114  9.17937 
.16138   .20785 
.17166   .23466 
.18197   .26000 
.19232   .28402 

6.6166  0.82063 
6.1966   .79211; 
5.8256   .76534 
54954   .74000 
S-I997   -71598 

o8°36' 
09  10 

0944 
10  19 

1053 

0.20 
.21 

.22 

•23 
.24 

0.19867  9.29813 
.20846   -31902 
.21823   .33891 
•22798   -35789 
•23770   .37603 

0.98007  9.99126 
.97803   .99035 
.97590   .98940 
•97367   .98841 
.97134   .98737 

0.20271  9.30688 
.21314   .32867 
.22362   .34951 
.23414   .36948 
.24472   .38866 

4-9332  0.69312 
4.6917   .67133 
4.4719   .65049 
4.2709   .63052 
4.0864   .61134 

II°28' 
12  02 
12  36 
I3  II 
1345 

°:ll 
:% 

.29 

0.24740  9.39341 
.25708   .41007 
.26673   .42607 
.27636   .44147 
.28595   .45629 

0.96891  9.98628 

•96639   -98515 
.96377   .98397 
.96106   .98275 
.95824   .98148 

0-25534  9-40712 
.26602   42491 
.27676   .44210 
.28755   -45872 
.29841   47482 

3.9163  0.59288 
3-7592   .57509 
3-6i33   .55790 
3.4776   .54128 
3.3511   .52518 

I4°i9' 

H  54 
15  28 
16  03 
1637 

0.30 
•31 
•32 
•33 
•34 

0-29552  9.47059 
.30506   .48438 

•3'457   -49771 
.32404   .51060 

•33349   -52308 

0-95534  9-98016 
•95233   -97879 
.94924   .97737 
.94604   .97591 
.94275   .97440 

0.30934  9.49043 
•32033   '50559 
.33139   .52034 
.34252   .53469 
-35374   .54868 

3.2327  0.50957 
3.1218   49441 
3.0176   47966 
2.9195   46531 
2.8270   45132 

17°!  i' 
17  46 
18  20 

1854 
19  29 

o-35 
•36 

i 

•39 

0.34290  9.53516 
•35227   .54688 
.36162   .55825 
.37092   .56928 
.38019   .58000 

0-93937  9-97284 
•9359°   -97123 
•93233   .96957 
.92866   .96786 
.92491   .96610 

0-36503  9-56233 
.37640   .57565 
.38786   .58868 
.39941   .60142 
41105   .61390 

2-7395  0.43767 
2.6567   42435 
2.5782   41132 

2-5037   .39858 
2.4328   .38610 

20°03' 
20  38 
21  12 
21  46 
22  21 

0.40 
.41 
.42 
•43 
•44 

0.38942  9.59042 
.39861   .60055 
.40776   .61041 
41687   .62000 
.42594   .62935 

0.92106  9.96429 
.91712   .96243 
.91309   .96051 
•90897   -95855 
•90475   -95653 

0.42279  9.62-613 
43463   .63812 
44657   .64989 
.45862   .66145 
47078   .67282 

2.3652  0.37387 
2.3008   .36188 

2.2393   -350II 
2.1804   .33853 
2.1241   .32718 

22°55' 
23  29 
24  04 
2438 
25  13 

o.4S 
.46 

•47 
.48 

•49 

0.43497  9-63845 
.44395   .64733 
45289   .65599 
.46178   .66443 
47063   .67268 

0.90045  9.95446 
.89605   .95233 
.89157   -95015 
.88699   -94792 
-88233   .94563 

0.48306  9.68400 
•49545   .69500 
•50797   -70583 
.52061   .71651 

•53339   -72704 

2.0702  0.31600 
2.0184   .30500 
1.9686   .29417 
1.9208   .28349 
1.8748   .27296 

25°47' 

26  21 
2656 
27  30 
28  04 

o  50 

0-47943  9-68072 

0.87758  9-94329 

0.54630  973743 

1.8305  0.26257 

28°39' 

SMITHSONIAN  TABLES. 


*  Arranged  and  computed  by  C.  E.  Van  Orstraud. 


TABLE    i  2  (continued). 

CIRCULAR  (TRIGONOMETRIC)  FUNCTIONS. 


RADIANS. 

SINES. 

COSINES. 

TANGENTS. 

COTANGENTS. 

DEGREES. 

Nat.     Log. 

Nat.     Log. 

Nat.     Log. 

Nat.      Log. 

0.50 
•51 
•52 
•53 
•54 

0-47943   9-68072 
.48818   .68858 
.49688   .69625 

•50553   70375 
.51414   71108 

0.87758   9.94329 
.87274    .94089 
.86782    .93843 
.86281    .93591 
•85771    -93334 

0.54630  973743 
•55936   74769 
•57256   75782 
.58592   .76784 
•59943   77774 

1.8305    0.26257 
7878     .25231 
.7465     .24218 
.7067     .23216 
.6683     .22226 

29  U 
2948 

3O  22 
3056 

-59 

0.52269  9.71824 
.53119   72525 
•53963   73210 
.54802   73880 
.55636   74536 

0.85252   9.93071 
.84726   .92801 
.84190   .92526 
.83646   .92245 
.83094    .91957 

0.61311  978754 
.62695   79723 
.64097   .80684 
•65517   -81635 
.66956   .82579 

1.6310    0.21246 

.5950    .20277 
.5601     .19316 
.5263     .18365 
.4935     -I742I 

3205 
32  40 

33  14 
3348 

0.60 
.61 
.62 

•63 
.64 

0.56464  975T77 
.57287   75805 
.58104   76420 
•589H   77022 
.59720   .77612 

0.82534   9.91663 
.81965    .91363 
.81388    .91056 
.80803    -90743 
.80210    .90423 

0.68414  9.83514 
.69892   .84443 

•7I391   -85364 
.72911   .86280 
74454   .87189 

1.4617    0.16486 
•43°8     .15557 
.4007     .14636 
'3715     -13720 
.3431     .12811 

34°23' 

34  57 

3606 
3640 

1 

0.60519  9.78189 
.61312   78754 
.62099   79308 
.62879   79851 
.63654   .80382 

0.79608   9.90096 
.78999   .89762 
.78382    .89422 

•77757   -89074 
.77125   .88719 

076020  9.88093 
77610   .88992 
79225   .89886 
.80866   .90777 
.82534   .91663 

1.3154    0.11907 
.2885     .11008 
.2622     .10114 
.2366     .09223 
.2Il6    .08337 

3749 
3823 
3858 
3932 

0.70 

72 
73 
74 

0.64422  9.80903 
.65183   .81414 
.65938   .81914 
.66687   -82404 
.67429   .82885 

076484  9.88357 
.75836   .87988 
75181   .87611 
74517   .87226 
.73847   .86833 

0.84229  9.92546 
•85953   -93426 
•87707   -94303 
.89492   .95178 
.91309   .96051 

1.1872    0.07454 
.1634     .06574 
.1402     .05697 
.1174     .04822 
.0952     .03949 

40°o6' 
40  41 
41  15 

41  5° 
42  24 

075 
76 

9 

79 

0.68164  9.83355 
.68892   .83817 
.69614   .84269 
.70328   .84713 
.71035   .85147 

073169  9.86433 
.72484   .86024 
.71791   .85607 
.71091   .85182 
-70385   .84748 

0.93160  9.96923 

•95045   -97793 
.96967   .98662 
.98926  9.9953  1 
i  .0092   0.00400 

1.0734    0.03077 
.0521     .02207 
.0313     .01338 
1.0109    .00469 
0.99084   9.99600 

42°58' 

4333 
44  07 
44  41 
45  l6 

0.80 
.81 
.82 

0.71736  9.85573 
.72429   .85991 
.73115   .86400 
73793   -86802 
.74464   .87195 

0.69671   9.84305 
.68950   .83853 
.68222   .83393 
.67488   .82922 
.66746   .82443 

1.0296   0.01268 
.0505    .02138 
.0717    .03008 
.0934    .03879 
.1156    .04752 

0.97121   9.98732 

•95T97   -97862 
•93309   -96992 
.91455   .96121 

•89635   -95248 

45°5o' 
4628 
46  59 
47  33 
48  08 

.'87 
.88 
.89 

075128  9.87580 
75784   .87958 
.76433   .88328 
77074   .88691 
.77707   .89046 

0.65998  9.81953 
.65244   .81454 
.64483   .80944 
.63715   .80424 
.62941   .79894 

1.1383   0.05627 
.1616    .06504 
-1853    .07384 
.2097    .08266 
.2346    .09153 

0.87848  9.94373 
.86091   -93496 
.84365   .92616 
.82668   .91734 
.80998   .90847 

49  16 
49  51 
5°  25 
51  oo 

0.90 
.91 
.92 
•93 
•94 

078333  9-89394 
7895°   -89735 
.79560   .90070 
.80162   .90397 
.80756   .90717 

0.62161  979352 

•61375   78799 
.60582   78234 

•59783   77658 
.58979   77070 

1.2602   0.10043 
.2864    .10937 
•3*33    -"835 
.3409    .12739 
.3692    .13648 

079355  9-89957 
7773s   .89063 
.76146   .88165 
.74578   .87261 
73034   .86352 

5'034' 
52  08 

52  43 
53  17 
53  5i 

0-95 
.96 

•97 
•98 
•99 

0.81342  9.91031 
.81919   .91339 
.82489   .91639 
.83050   .91934 
.83603   .92222 

0.58168  9.76469 

•57352   75855 
.56530   .75228 
.55702   .74587 
•54869   73933 

1.3984   0.14563 
.4284    .15484 
.4592    .16412 
.4910    .17347 
.5237    .18289 

0.71511  9.85437 
.70010   -84516 
.68531   .83588 
.67071   .82653 
.65631   .81711 

54°26' 

5535 
5609 

5643 

1.  00 

0.84147  9.92504 

0.54030  973264 

J-5574   0.19240 

0.64209  9.80760 

57°i8' 

SMITHSONIAN  TABLES. 


TABLE    12  (continued), 
CIRCULAR  (TRIGONOMETRIC)  FUNCTIONS. 


RADIANS.  II 

SINES. 

COSINES. 

TANGENTS. 

COTANGENTS. 

DEGREES. 

Nat.     Log- 

Nat.     Log. 

Nat.     Log. 

Nat.     Log, 

1.  00 
.Ol 

.02 

•03 
.04 

0.84147   9.92504 
.84683    .92780 
.85211    .93049 

•8573°   -933  i  3 
.86240   .93571 

0.54030   9.73264 
.53186   .72580 
•52337    -71881 
.51482   .71165 
.50622   .70434 

1.5574   0.19240 

.5922    .20200 
.6281    ,2Il69 
.6652    .22148 
.7036    .23137 

0.64209  9.80760 
.62806  .79800 
.61420  .78831 
.60051  .77852 
.58699  .76863 

57°i8' 
57  52 
5827 
59oi 
5935 

•a 
a 

.09 

0.86742  9.93823 
.87236   .94069 
.87720   -94310 
.88196   .94545 
.88663   -94774 

0-49757  9-69686 
.48887   .68920 
.48012   -68135 

•47133   -67332 
.46249   .66510 

1.7433   0.24138 
.7844    .25150 
.8270    -26175 
.8712    .27212 
.9171    .28264 

0.57362  9-75862 
.56040  .74850 

•54734  .73825 
.53441  .72788 
.52162  .71736 

6o°io' 
6044 
61  18 

61  53 
62  27 

I.IO 

.11 

.12 

•J3 

.14 

0.89121  9.94998 
.89570   .95216 
.90010   -95429 
.90441   .95637 
.90863   .95839 

0.45360  9.65667 
.44466   .64803 
.43568   -63917 
.42666   .63008 
.41759   .62075 

1.9648   0,29331 
2.0143    .30413 
.0660    .31512 
.1197    .32628 
..1759    .33763 

0.50897  '  9.70669 
.49644  .69587 
.48404  .68488 
.47175  -67372 
•45959  -66237 

63°o2' 
6336 
64  10 
64  45 
65  19 

"i 

.16 

•17 
.18 
.19 

0.91276  9-96036 
.91680   .96228 
.92075   .96414 
.92461   -96596 
.92837   .96772 

0.40849  9.61118 
-39934   -60134 
•39015   -59123 
.38092   .58084 
.37166   .57015 

2.234C   0.34918 
.2958    .36093 
.3600    .37291 
.4273    .38512 

•4979   -39757 

0-44753  9-65082 
43558  -63907 
.42373  .62709 
.41199  .61488 
,40034  .60243 

65°53' 
6628 
67  02 

67  37 
68  ii 

i.  20 

.21 
.22 

•23 
.24 

0.93204  9-96943 
•93562   .97110 
.93910   .97271 
.94249   .97428 
•94578   -97579 

0.36236  9.55914 

•353°2   .54780 
•34365   -53611 
.33424   .52406 
.32480   .51161 

2.5722  0.41030 
.6503   .42330 
.7328   .43660 
.8198   .45022 
.9119   .46418 

0.38878  9.58970 
•37731  -57670 
.36593  -56340 
•35463  .54978 
•34341  -53582 

68°45' 
69  20 
6954 
70  28 
7i  03 

•a 

.27 
.28 
.29 

0.94898  9.97726 
.95209   .97868 
.95510   .98005 
.95802   .98137 
.96084   .98265 

o-3  r  532  949875 
.30582   .48546 
.29628   .47170 
.28672   .45745 
.27712   .44267 

3.0096  0.47850 
•"33   -49322 
.2236   .50835 

•3413   -52392 
.4672   .53998 

o.33227  9-52I5° 
.32121  .50678 
.31021  .49165 
.29928  .47608 
.28842  .46002 

7i°37' 
72  12 

'72  46 
73  20 
73  55 

1.30 
•31 
•32 

•33 
•34 

0.96356  9-98388 
.96618   .98506 
.96872   .98620 
.97115   .98729 
•97348   -98833 

0.26750  9.42732 
.25785   .41137 
.24818   .39476 
.23848   .37744 
•22875   .35937 

3.6021  0.55656 
•7471   -57369 
.9033   «59*44 
4.0723   .60984 
.2556   .62896 

0.27762  944344 
.26687  -42631 
.25619  .40856 
.24556  .39016 
•23498  .37104 

74°29' 
7503 
7538 

76  12 
7647 

'3 
9 

•39 

0-97572  9-98933 
.97786   .99028 
.97991   .99119 
.98185   .99205 
.98370   .99286 

0.21901  9.34046 
.20924   .32064 
.19945   .29983 
.18964   .27793 
.17981   .25482 

4.4552  0.64887 
.6734   .66964 
.9131   .69135 
5.1774   .71411 
.4707   .73804 

0.22446  9-35113 
.21398  .33036 
.20354  .30865 
.19315  .28589 
.18279  .26196 

77°2i' 
77  55 
7830 

79  °4 
7938 

1.40 
.41 
.42 
•43 
•44 

0-98545  9-99363 
.98710   .99436 
.98865   .99504 
.99010   .99568 
.99146   .99627 

0.16997  9.23036 
.16010   .20440 
.15023   .17674 
.14033   .14716 
.13042   .11536 

5-7979  0.76327 
6.1654   .78996 
6.5811   .81830 
7.0555   .84853 
7.6018   .88092 

0.17248  9.23673 
.16220  .21004 
.15195  .18170 
.14173  .15147 
.13155  .11908 

8o°i3' 
8047 

8l  22 

81  56 
82  30 

MS 

.46 

48 
.49 

0.99271  9.99682 

•99387   -99733 
.99492   .99779 
.99588   .99821 
.99674   .99858 

0.12050  9.08100 
.11057   .04364 
.10063   .00271 
.09067  8.95747 
.0807  1   .90692 

8.2381  0.91583 
8.9886   .95369 
9.8874   .99508 
10.983   1.04074 
12.350    .09166 

0.12139  9.08417 
.11125  .04631 
.10114  .00492 
.09105  8.95926 
.08097  .90834 

83°o5' 
8339 
84  13 
8448 

85  22 

1.50 

0-99749  9-9989I 

0.07074  8.84965 

14.101   1.14926 

0.07091  8.85074 

85°57' 

SMITHSONIAN  TABLES. 


TABLES   1  2  (continued)  AND  1  2A. 
CIRCULAR  FUNCTIONS  AND  FACTORIALS. 

TABLE  12  (continued).  —  Circular  (Trigonometric)  Functions. 


RADIANS. 

SINES. 

COSINES. 

TANGENTS. 

COTANGENTS. 

DEGREES.  1 

Nat.            Log. 

Nat.             Log. 

Nat.            Log. 

Nat.            Log. 

1.50 

•52 
•53 
•54 

0.99749     9.99891 
.99815       .99920 
.99871        .99944 
.99917        .99964 

•99953      -99979 

0.07074     8.84965 
.06076       .78361 
.05077        .70565 
.04079       .61050 
.03079       .48843 

14.101      1.14926 
16.428       .21559 
19.670       .29379 
24.498       .38914 
32.461        .51136 

0.07091     8.85074 
.06087        .78441 
.05084       .70621 
.04082       .61086 
.03081        .48864 

S5°57' 
8631 
87  05 
87  40 
88  14 

•56 

$ 

•59 

0.99978    9.99991 
0.99994    9-99997 

I  .OOOOO      O.OOOOO 

0.99996  9.99998 
0.99982  9-99992 

0.02079     8.31796 
.01080     8.03327 
.00080     6.90109 
-.00920    7.96396n 
-.01920    8.2833611 

48.078     1.68195 
92.621      1.96671 
1255.8          3.09891 
108.65        2.03603 
52.067      1.71656 

0.02o8o     8.31805 
.01080     8.03330 
.00080     6.90109 
-.00920    7.  96397  n 
-.01921     8.28344n 

88°49' 
8923 
8957 
9032 
91  06 

1.60 

0-99957    9-9998i 

-0.02920    8.46538n 

34-233     1-53444 

-0.02921    8-46556n 

9i°4o' 

90°=  i. 570  7963  radians. 


TABLE  12a. -Factorials. 

Logarithms  of  the  products  1.2.3 w»  n  ^rom  i  to  100. 

See  Table  30  for  log.  T  (n  + 1 ),  values  of  n  between  i  and  2. 


n. 

!*(-> 

n. 

£W> 

n. 

log.(«0 

n. 

•*w 

1 

o.oooooo 

26 

26.605619 

51 

66.190645 

76 

111.275425 

2 

0.301029 

27 

28.036982 

52 

67.906648 

77 

113.161916 

3 

0.778151 

28 

29.484140 

53 

69.630924 

78 

115.054010 

4 

1.380211 

29 

30.946538 

54 

71.363318 

79 

116.951637 

5 

2.079181 

30 

32.423660 

55 

73.103680 

80 

118.854727 

6 

2.857332 

31 

33-9I502I 

56 

74.851868 

81 

120.763212 

7 

3.702430 

32 

35.420171 

57 

76.607743 

82 

122.677026 

8 

4.605520 

33 

36.938685 

58 

78.371171 

83 

124.596104 

9 

10 

5-559763 
6.559763 

34 
35 

38.470164 
40.014232 

59 
60 

80.142023 
81.920174 

84 

85 

126.520383 
128.449802 

11 

12 

7.601155 
8.680336 

36 

37 

4L570535 
43-T38736 

61 

62 

83.705504 
85.497896 

86 

87 

1  30-38430  1 
132.323820 

13 

9.794280 

10.940408 

38 
39 

44.718520 
46.309585 

63 
64 

87.297236 
89.103416 

88 
89 

134.268303 
136.217693 

15 

12.116499 

40 

47.911645 

65 

90.916330 

90 

I38.I7I935 

16 

13.320619 

41 

49.524428 

66 

92.735874 

91 

140.130977 

17 

14.551068 

42 

51.147678 

67 

94.561948 

92 

142.094765 

18 

15.806341 

43 

52.781146 

68 

96-394457 

93 

144.063247 

19 

17.085094 

44 

54.424599 

69 

98.233306 

94 

146.036375 

20 

18.386124 

45 

56.07781  1 

70 

100.078405 

95 

148.014099 

21 

19.708343 

46 

57.740569 

71 

101.929663 

96 

149.996370 

22 

21.050766 

47 

59.412667 

72 

103.786995 

97 

151.983142 

23 

22.412494 

48 

61.093908 

73 

105.650318 

98 

'53-974368 

24 

23-792705 

49 

62.784104 

74 

I°7-5I955° 

99 

155.970003 

25 

25.190645 

5° 

64.483074 

75 

109.394611 

IOO 

157.970003 

SMITHSONIAN  TABLES. 


TABLE  13. 
HYPERBOLIC  FUNCTIONS.* 

Hyperbolic  sines.  Values  of 


39 


0 

0 

1 

2 

3 

4 

5 

6 

7 

•8 

9 

0.0 

o.oooo 

O.OIOO 

O.02OO 

0.0300 

0.0400 

0.0500 

0.0600 

0.0701 

0.0801 

0.0901 

OJ 

.1002 

.IIO2 

.I2O3 

.1304 

.1405 

.1506 

.1607 

.1708 

.1810 

.1911 

0.2 

.2013 

.2115 

.2218 

.2320 

.2423 

.2526 

.2629 

•2733 

•2837 

.2941 

o-3 

•3°45 

•3150 

•3255 

•336o 

•3466 

•3572 

.3678 

•3785 

.3892 

.4000 

0.4 

.4108 

.4216 

•4325 

•4434 

•4543 

•4653 

•4764 

•4875 

.4986 

.5098 

0.5 

0.6 

0.7 

0.5211 
.6367 

°'P«4 
.6485 

.7712 

0.5438 
.6605 
.7838 

0-5552 
•6725 
.7966 

0.5666 
.6846 
.8094 

°:$* 

.8223 

0.5897 
.7090 
•8353 

0.6014 
.7213 
.8484 

0.6131 

•7336 
.8615 

0.6248 
.7461 
.8748 

0.8 

.8881 

.9015 

.9150 

.9286 

•9423 

.9561 

.9700 

.9840 

.9981 

.0122 

0.9 

1.0265 

1.0409 

1-0554 

1.0700 

1.0847 

1.0995 

1.1144 

1.1294 

1.1446 

1.1598 

1.0 

1.1752 

I.I907 

1.2063 

I.222O 

1-2379 

1-2539 

1.2700 

1.2862 

1.3025 

1.3190 

i.i 

•3356 

•3524 

-3693 

•3863 

•4035 

.4208 

.4382 

•4558 

•4735 

.4914 

1.2 

•5°95 

.5276 

.5460 

•5645 

•5831 

.6019 

.6209 

.6400 

•6593 

.6788 

i-3 

.6984 

.7182 

.7381 

•7583 

•7786 

.7991 

.8198 

.8406 

.8617 

.8829 

1.4 

•9043 

•9259 

•9477 

.9697 

.9919 

2.0143 

2.0369 

2.0597 

2.0827 

2.1059 

1.5 

2.1293 

2.1529 

2.1768 

2.2008 

2.2251 

2.2496 

2.2743 

2.2993 

2-3245 

2-3499 

1.6 

i-7 

•3756 
.6456 

.4015 
.6740 

.4276 
.7027 

•4540 
•7317 

.4806 
.7609 

•5075 
•7904 

•5346 
.8202 

.5620 
•8503 

Jsol 

•6175 
.9112 

1.8 

.9422 

•9734 

3.0049 

3-0367 

3.0689 

3-IOI3 

3-J340 

3.1671 

3.2005 

3-234I 

1.9 

3.2682 

3-3025 

•3372 

.3722 

•4075 

•4432 

•4792 

•5156 

•5523 

.5894 

2.0 

3.6269 

3.6647 

3.7028 

3-74I4 

3-7803 

3.8196 

3-8593 

3-8993 

3-9398 

3.9806 

2.1 

4.0219 

4-0635 

4.1056 

4.1480 

4.1909 

4-2342 

4.2779 

4.3221 

4.3666 

4.4117 

2.2 

4-4571 

4-5030 

4-5494 

4.5962 

4.6434 

4.6912 

4-7394 

4.7880 

4.8372 

4.8868 

2-3 
2.4 

4-9370 
5.4662 

4.9876 
5.5221 

5-0387 
5-5785 

5-0903 
5-6354 

5-I425 
5.6929 

5-I951 
5-75Jo 

5-2483 
5.8097 

5.3020 
5.8689 

5-3562 
5.9288 

5.4109 
5-9892 

2.5 

2.6 

6.0502 
6.6947 

6.1118 
6.7628 

6.1741 
6-8315 

6.2369 
6.9009 

6.3004 
6.9709 

6-3645 
7.0417 

6.4293 
7.1132 

6.4946 
7-1854 

6.5607 
7-2583 

6.6274 
7-33I9 

2.7 

7.4063 

7.4814 

7-5572 

7.6338 

7.7112 

7.7894 

7-8683 

7.9480 

8.0285 

8.1098 

2.8 

2.9 

8.1919 
9.0596 

8.2749 
9.1512 

8.3586 
9-2437 

8.4432 
9-3371 

8.5287 
9-43I5 

8.61  50 
9.5268 

8.7021 
9.6231 

8.7902 
9.7203 

8.8791 
9.8185 

8.9689 
9-9I77 

3.0 

10.018 

10.119 

IO.22I 

10.324 

11.429 

JI-534 

11.640 

11.748 

11.856 

11.966 

3-i 

11.076 

11.188 

11.301 

II.4I5 

n-530 

12.647 

12.764 

12.883 

12.003 

12.124 

3-2 

12.246 

12.369 

12.494 

12.620 

12.747 

12.876 

13.006 

I3-I37 

13.269 

1  3-403 

3-3 

I3-538 

I3-674 

I3.8I2 

J3-95I 

14.092 

14.234 

14-377 

14.522 

14.668 

14.816 

34 

14.965 

15.116 

15.268 

15.422 

15-577 

15-734 

I5-893 

16.053 

16.214 

16.378 

3.5 

16.543 

16.709 

16.877 

17.047 

17.219 

17-392 

17-567 

17-744 

17-923 

18.103 

3-6 

18.285 

18.470 

18-655 

18.843 

1  9-°33 

19.224 

19.418 

19.613 

19.811 

2O.OIO 

3i 

2O.2II 

20.415 

2O.62O 

20.828 

21.037 

21.249 

21.463 

21.679 

21.897 

22.117 

3-8 

22.339 

22.564 

22.791 

23.020 

23.252 

23.486 

23.722 

23.961 

24.202 

24.445 

3-9 

24.691 

24.939 

25.190 

25.444 

25.700 

25.958 

26.219 

26.483 

26.749 

27.018 

4.0 

27.290 

27.564 

27.842 

28.122 

28.404 

28.690 

28.979 

29.270 

29-564 

29.862 

4.1 

30.162 

30-465 

30.772 

31.081 

31-393 

31.709 

32.028 

32.350 

32-675 

33-004 

4.2 

33-336 

33-67I 

34.009 

34-351 

34-697 

35-046 

35-398 

35-754 

36-113 

36.476 

4-3 

36.843 

37-214 

37.588 

37.966 

38.347 

38.733 

39.122 

39-5J5 

39-9»3 

40.314 

4.4 

40.719 

41.129 

41.542 

41.960 

42-382 

42.808 

43-238 

43-673 

44.112 

44-555 

4.5 

45-003 

45-455 

45-912 

46.374 

46.840 

47-311 

47-787 

48.267 

48.752 

49.242 

4.6 

49-737 

50-237 

50.742 

51.252 

5^767 

52.288 

52-813 

53-344 

53.880 

54.422 

4-7 

54.969 

55.522 

56.080 

56-643 

57-213 

57788 

58.369 

58-955 

59-548 

60.147 

4.8 

60.751 

61.362 

61.979 

62.601 

63-231 

63.866 

64.508 

65-I57 

65.812 

66.473 

4.9 

67.141 

67.816 

68.498 

69.186 

69.882 

70.584 

71.293 

72.010 

72-734 

73-465 

*  Tables  38-41  are  quoted  from  "  Des  Ingenieurs  Taschenbuch,"  herausgegeben  vom  Akademischen  Verein  (Hiitte). 
SMITHSONIAN  TABLES. 


TABLE  14. 
HYPERBOLIC   FUNCTIONS. 

Common  logarithms  -f  10  of  the  hyperbolic  sines. 


as 

o" 

1 

2 

3 

4 

5 

6 

7 

8 

9 

0.0 

00 

8.0000 

3011 

4772 

6022 

6992 

7784 

8455 

9036 

9548 

O.I 

9.0007 

0423 

0802 

1152 

1475 

1777 

2060 

2325 

2576 

2814 

O.2 

3°39 

3254 

3459 

3656 

3844 

4025 

4199 

4366 

4528 

4685 

0.4 

9.6136 

4983 
6249 

5^25 
6359 

5264 
6468 

5398 
6574 

3$ 

5656 
6780 

578i 
6880 

5902 
6978 

6020 
7074 

0.5 

9.7169 

7262 

7354 

7444 

7533 

7620 

7707 

7791 

7875 

7958 

0.6 

8039 

8119 

8199 

8277 

8334 

8431 

8506 

8581 

8655 

8728 

0.7 

8800 

8872 

8942 

9012 

9082 

9150 

9218 

9286 

9353 

9419 

0.8 

9485 

9550 

9614 

9678 

9742 

9805 

9868 

9930 

9992 

°°53 

0.9 

10.0114 

0174 

0234 

0294 

0353 

0412 

0470 

0529 

0586 

0644 

1.0 

10.0701 

0758 

0815 

0871 

0927 

0982 

1038 

1093 

1148 

1203 

i.i 

1257 

1311 

1365 

1419 

1472 

1525 

1578 

1631 

1684 

1736 

1.2 

1788 

1840 

1892 

1944 

I995 

2046 

2098 

2148 

2199 

2250 

1.3 

2300 

2351 

2401 

2451 

2501 

2551 

2600 

2650 

2699 

2748 

1.4 

2797 

2846 

2895 

2944 

2993 

304i 

3090 

3138 

3186 

3234 

1.5 

10.3282 

3330 

3378 

3426 

3474 

3521 

3569 

3616 

3663 

37H 

1.6 

3758 

3805 

3852 

3899 

3946 

3992 

4039 

4086 

4J32 

i-7 

4225 

4272 

4364 

4411 

4457 

45°3 

4549 

4595 

4641. 

1.8 

4687 

4733 

4778 

4824 

4870 

49*5 

4961 

5007 

5052 

5098 

1.9 

5H3 

5188 

5234 

5279 

5324 

5370 

5415 

5460 

55°5 

5550 

2.0 

2.1 

10.5595 
6044 

5640 
6089 

5685 
6134 

5730 
6178 

5775 
6223 

5820 
6268 

5865 
6312 

59™ 
6357 

5955 
6401 

5999 
6446 

2.2 

6491 

6535 

6580 

6624 

6668 

6713 

6757 

6802 

6846 

6890 

2-3 

6935 

6979 

7023 

7067 

7112 

7156 

7200 

7244 

7289 

7333 

2.4 

7377 

7421 

7465 

7509 

7553 

7597 

7642 

7686 

773° 

7774 

2.5 

10.7818 

7862 

7906 

795° 

7994 

8038 

8082 

8126 

8169 

8213 

2.6 

8257 

8301 

8345 

8389 

8433 

8477 

8521 

8564 

8608 

8652 

2.7 

8696 

8740 

8784 

8827 

8871 

8915 

8959 

9003 

9046 

9090 

2.8 

9134 

9178 

9221 

9265 

9309 

9353 

9396 

9440 

9484 

9527 

2.9 

957i 

9615 

9658 

9702 

9746 

9789 

9833 

9877 

9920 

9964 

3.0 

11.0008 

0051 

0095 

0139 

0182 

0226 

0270 

0313 

°357 

0400 

3-1 

0444 

0488 

0531 

°575 

0618 

0662 

0706 

0749 

0793 

0836 

3-2 

0880 

0923 

0967 

ion 

1054 

1098 

1141 

1185 

1228 

1272 

3-3 

1316 

1359 

1403 

1446 

1490 

1533 

1577 

1620 

1664 

1707 

3-4 

I751 

1794 

1838 

1881 

1925 

1968 

2OI2 

2056 

2099 

2143 

3.5 

11.2186 

2230 

2273 

2317 

2360 

2404 

2447 

2491 

2534 

2578 

3-6 

2621 

2665 

2708 

2752 

2795 

2839 

2882 

2925 

2969 

3012 

3-7 

3056 

3°99 

3H3 

3186 

3230 

3273 

3317 

3360 

3404 

3447 

3-8 

3534 

3578 

3621 

3665 

3708 

3752 

3795 

3838 

3882 

3-9 

3925 

3969 

4012 

4056 

4099 

4H3 

4186 

4230 

4273 

4317 

4.0 

11.4360 

4403 

4447 

4490 

4534 

4577 

4621 

4664 

4708 

4751 

4.1 

4795 

4838 

4881 

4925 

4968 

5012 

5055 

5°99 

5H2 

5186 

4.2 

5229 

5273 

5316 

5359 

5403 

5446 

5490 

5533 

5577 

5620 

4-3 

4.4 

5707 
6141 

575° 
6185 

5794 

5837 
6272 

5881 
6315 

5924 
6359 

5968 
6402 

6011 
6446 

6055 
6489 

4.5 

11.6532 

6576 

6619 

6663 

6706 

6750 

6793 

6836 

6880 

6923' 

4.6 

6967 

7010 

7054 

7097 

7141 

7184 

7227 

7271 

73J4 

7358 

4-7 

7401 

7445 

7488 

7531 

7575 

7618 

7662 

7705 

7749 

7792 

4.8 

7836 

7879 

7922 

7966 

8009 

8053 

8096 

8140 

8183 

8226 

4.9 

8270 

8313 

8357 

8400 

8444 

8487 

8530 

8574 

8617 

8661 

SMITHSONIAN  TABLES. 


TABLE  1 5. 
HYPERBOLIC  FUNCTIONS. 

Hyperbolic  cosines.  Values  of 


• 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

0.0 

1.  0000 

1.  000  1 

1.0002 

1.0005 

1.0008 

1.0013 

1.0018 

1.0025 

1.0032 

1.0041 

O.I 

.0050 

.0061 

.OO72 

.0085 

.0098 

.0113 

.0128 

.0145 

.0162 

.0181 

O.2 

.0201 

.0221 

.0243 

.0266 

.0289 

.0314 

.0340 

.0367 

•0395 

.0423 

o-3 

•0453 

.0484 

.0516 

.0549 

.0584 

.0619 

•0655 

.0692 

.0731 

.0770 

0.4 

.0811 

.0852 

•0895 

.0939 

.0984 

.1030 

.1077 

.1125 

.1174 

.1225 

0.5 

1.1276 

1.1329 

LI383 

1.1438 

1.1494 

I.I55I 

1.1609 

1.1669 

1.1730 

1.1792 

0.6 

•1855 

.1919 

.1984 

.2051 

.2119 

.2188 

.2258 

•2330 

.2402 

.2476 

0.7 

•2552 

.2628 

.2706 

.2785 

.2865 

•2947 

•3030 

•3114 

•3J99 

.3286 

0.8 

•3374 

•3464 

-3555 

•3647 

-3740 

•3835 

•3932 

.4029 

.4128 

.4229 

0.9 

433  i 

4434 

4539 

.4645 

4753 

.4862 

4973 

.5085 

•5199 

•5314 

1.0 

i-543i 

1-5549 

1.5669 

1-5790 

J-59I3 

1.6038 

.6164 

1.6292 

1.6421 

1.6552 

.1 

.2 

.6685 
.8107 

.6820 
.8258 

!S4?2 

.7093 
.8568 

•7233 

.8725 

•m 

.7517 
•9045 

.7662 
.9208 

.7808 
•9373 

•7956 
-9540 

•3 

.9709 

.9880 

2.0053 

2.0228 

2.0404 

2.0583 

2.0764 

2.0947 

2.1132 

2.1320 

4 

2.1509 

.1700 

.1894 

T2090 

.2288 

.2488 

.2691 

.2896 

•3!03 

•3312 

1.5 

2.3524 

2.3738 

2.3955 

2.4174 

2-4395 

2.4619 

2.4845 

2.5073 

2-5305 

2.5538 

.6 

•5775 

•6013 

•6255 

•6499 

.6746 

•6995 

•7247 

.7502 

.7760 

.8020 

•7 

.8283 

.8549 

.8818 

.9090 

-9364 

.9642 

.9922 

3.0206 

3.0492 

3.0782 

1.8 

3-^075 

3-i37i 

3-1669 

3.1972 

3.2277 

3-2585 

3.2897 

.3212 

•353° 

•3852 

1.9 

4177 

.4506 

4838 

•5'73 

•5512 

•5855 

.6201 

•6551 

.6904 

.7261 

2.0 

3.7622 

37987 

3-8355 

3.8727 

3-9  i  03 

3-9483 

3.9867 

4-0255 

4.0647 

4.1043 

2.1 

4-1443 

4.1847 

4.2256 

4.2668 

4-3085 

4-3507 

4-3932 

4.4362 

4-4797 

4-5236 

2.2 

4-  5679 

4.6127 

4.6580 

4-7037 

4-7499 

4.7966 

4.8437 

4.8914 

4-9395 

4.9881 

2-3 
2.4 

5-0372 
5-5569 

5.0868 
5.6119 

5-1370 
5.6674 

5-1876 
5-7235 

5.2388 
5-78oi 

5-2905 
5-8373 

5-3427 
5-895I 

5-3954 
5-9535 

5-4487 
6.0125 

5-5026 
6.0721 

2.5 

2.6 

6.1323 
6.7690 

6.1931 
6.8363 

6.2545 
6.9043 

6.3166 
6.9729 

6-3793 
7.0423 

6.4426 
7.1123 

6.5066 
7.1831 

6.5712 
7-2546 

6.6365 
7.3268 

6.7024 
7-3998 

3 

74735 
8.2527 

7-5479 
8-3351 

7.6231 

8.4182 

7.6990 
8.5022 

77758 
8.5871 

7-8533 
8.6728 

7.9316 
8.7594 

8.0106 
8.8469 

8.0905 
8.9352 

8.1712 
9.0244 

2.9 

9.1146 

9.2056 

9.2976 

9-3905 

9.4844 

9-5791 

9.6749 

9.7716 

9.8693 

9.9680 

3.0 

10.068 

10.168 

10.270 

10.373 

10.476 

10.581 

10.687 

10.794 

10.902 

1  1.  Oil 

3-i 

II.  121 

12.233 

"•345 

"459 

11.574 

11.689 

1  1.  806 

11.925 

12.044 

12.165 

3-2 

12.287 

12.410 

12.534 

12.660 

12.786 

12.915 

13.044 

I3-I75 

I3-307 

13.440 

3-3 

!3-575 

i3-7ii 

13.848 

13-987 

14.127 

14.269 

14.412 

14-556 

14.702 

14.850 

3-4 

14.999 

I5-I49 

I5-30I 

15455 

15.610 

15-766 

15.924 

16.084 

16.245 

16.408 

3.5 

16.573 

16.739 

16.907 

17.077 

17.248 

17.421 

I7-596 

17.772 

I7-951 

18.131 

3-6 

18.313 

18.497 

18.682 

18.870 

19.059 

19.250 

19.444 

19.639 

19.836 

20.035 

3-7 

20.236 

20.439 

20.644 

20.852 

21.061 

21.272 

21.486 

21.702 

21.919 

22.139 

3-8 

22.362 

22.586 

22.813 

23.042 

23-273 

23-507 

23-743 

23.982 

24.222 

24.466 

3-9 

24.711 

24.959 

25.210 

25.463 

25-719 

25-977 

26.238 

26.502 

26.768 

27.037 

4.0 

27.308 

27-582 

27.860 

28.139 

28.422 

28.707 

28.996 

29.287 

29.581 

29.878 

4.1 

30.178 

30.482 

30.788 

3I-°97 

31.409 

31-725 

32-044 

32.365 

32.691 

33019 

4.2 
4-3 
44 

33-351 
36-857 
40.732 

33-686 
37.227 
41.141 

34.024 
37.601 
4L554 

34.366 

37-979 
41.972 

34-7" 
38.360 
42.393 

35.060 
38.746 
42.819 

35412 
39-135 
43-25° 

35768 
39-528 
43.684 

36.127 

39-925 
44.123 

36.490 
40.326 
44.566 

4.5 

45.014 

45.466 

45-923 

46.385 

46.851 

47-321 

47-797 

48.277 

48.762 

49.252 

4.6 

49-747 

50.247 

50-752 

51.262 

5T-777 

52.297 

52.823 

53-354 

53-890 

54431 

4-7 
4.8 

54.978 
60.759 

55-531 
61.370 

56.089 
61.987 

56.652 
62.609 

57-221 

63.239 

57-796 
63.874 

64.516 

58.964 
65.164 

59-556 
65.819 

60.155 
66.481 

4-9 

67.149 

67.823 

68.505 

69.193 

69.889 

70.591 

71.300 

72.017 

72.741 

73472 

SMITHSONIAN  TABLES. 


TABLE  1  6. 
HYPERBOLIC   FUNCTIONS. 

Common  logarithms  of  the  hyperbolic  cosines. 


X 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

0.0 

o.oooo 

oooo 

OOOI 

OOO2 

0003 

0005 

0008 

OOII 

0014 

0018 

O.I 

0022 

0026 

0031 

0037 

0042 

0049 

0055 

0062 

0070 

0078 

0.2 

0086 

0095 

0104 

OII4 

0124 

0134 

0145 

0156 

0168 

0180 

°-3 

0193 

0205 

0219 

0232 

0246 

0261 

0276 

0291 

0306 

0322 

0.4 

0339 

0355 

0372 

0390 

0407 

0426 

0444 

0463 

0482 

0502 

0.5 

0.0522 

0542 

0562 

0583 

0605 

0626 

0648 

0670 

0693 

0716 

0.6 

0739 

0762 

0786 

0810 

0835 

0859 

0884 

0910 

0935 

0961 

0.7 

0987 

1013 

1040 

1067 

1094 

1122 

"49 

"77 

1206 

1234 

0.8 

1263 

1292 

1321 

'35° 

1380 

I4IO 

1440 

1470 

1501 

I532 

0.9 

1563 

1594 

1625 

1657 

1689 

1721 

1753 

1785 

1818 

1851 

1.0 

0.1884 

1917 

1950 

1984 

2018 

2O5I 

2086 

2I2O 

2154 

2189 

i.i 

2223 

2258 

2293 

2328 

2364 

2399 

2435 

2470 

2506 

2542 

1.2 

2578 

2615 

2651 

2688 

2724 

276! 

2798 

2835 

2872 

2909 

1.3 

2947 

2984 

3022 

3°59 

3°97 

3135 

3173 

321! 

3249 

3288 

1.4 

3326 

3365 

3403 

3442 

348i 

3559 

3598 

3637 

3676 

1.5 

0.3715 

3754 

3794 

3833 

3873 

3913 

3952 

3992 

4032 

4072 

1.6 

4112 

4152 

4192 

4232 

4273 

43J3 

4353 

4394 

4434 

4475 

1-7 

4515 

4556 

4597 

4637 

4678 

4719 

4760 

4801 

4842 

4883 

1.8 

4924 

4965 

5006 

5048 

5089 

5130 

5172 

5213 

5254 

5296 

1.9 

5337 

5379 

5421 

5462 

55°4 

5545 

5587 

5629 

5671 

5713 

2.0 

0.5754 

5796 

5838 

5880 

5922 

5964 

6006 

6048 

6090 

6132 

2.1 

2.2 

6175 
6597 

6217 
6640 

6259 
6682 

6301 
6724 

6343 
6767 

6386 
6809 

6428 
6852 

6470 
6894 

6512 
6937 

6555 
6979 

2-3 

7022 

7064 

7107 

715° 

7192 

7235 

7-278 

7320 

7363 

7406 

2.4 

7448 

749i 

7534 

7577 

7619 

7662 

7705 

7748 

7791 

7833 

2.5 

0.7876 

7919 

7962 

8005 

8048 

8091 

8i34 

8176 

8219 

8262 

2.6 

8305 

8348 

8391 

8434 

8477 

8520 

8563 

8606 

8649 

8692 

2-7 

8735 

8778 

8821 

8864 

8907 

8951 

8994 

9°37 

9080 

9123 

2.8 

9166 

9209 

9252 

9295 

9338 

9382 

9425 

9468 

95" 

9554 

2.9 

9597 

9641 

9684 

9727 

9770 

9813 

9856 

9900 

9943 

9986 

3.0 

1.0029 

0073 

0116 

0159 

0202 

0245 

0289 

0332 

0375 

0418 

3.1 

0462 

°5°5 

0548 

0591 

0635 

0678 

0721 

0764 

0808 

08  ci 

3-2 
3-3 

0894 
1327 

0938 
J37i 

0981 
1414 

1024 

1457 

1067 
I5OI 

mi 
1544 

"54 

1587 

"97 
1631 

1241 
1674 

1284 
1717 

3-4 

1761 

1804 

1847 

1891 

J934 

1977 

202  1 

2064 

2107 

2151 

3.5 

1.2194 

2237 

2281 

2324 

2367 

2411 

2454 

2497 

2541 

2584 

3-6 

2628 

2671 

2714 

2758 

2801 

2844 

2888 

2931 

2974 

3018 

3061 

3io5 

3*48 

3235 

3278 

3322 

3365 

3408 

3452 

3-8 

3495 

3538 

3582 

3625 

3712 

3755 

3799 

3842 

3886 

3-9 

3929 

3972 

4016 

4059 

4103 

4146 

4189 

4233 

4278 

4320 

4.0 

14363 

4406 

4450 

4493 

4537 

4580 

4623 

4667 

4710 

4754 

4.1 

4797 

4840 

4884 

4927 

497i 

5014 

5057 

5101 

5M4 

5188 

4.2 

5231 

5274 

5318 

5361 

5405 

5448 

5492 

5535 

5578 

5622 

4-3 
4.4 

5665 
6099 

5709 
6143 

3$ 

5795 
6230 

5839 
6273 

5882 
6316 

5926 
6360 

5969 
6403 

6012 
6447 

6056 
6490 

4.5 

I-6533 

6577 

6620 

6664 

6707 

6751 

6794 

6837 

6881 

6924 

4.6 

6968 

7011 

7055 

7098 

7141 

7185 

7228 

7272 

7315 

7358 

4-7 

7402 

7445 

7489 

7532 

7576 

7619 

7662 

7706 

7749 

7793 

4.8 

7836 

7880 

7923 

7966 

8010 

8053 

8097 

8140 

8184 

8227 

4.9 

8270 

8314 

8357 

8401 

8444 

8487 

8574 

8618 

8661 

SMITHSONIAN  TABLES. 


TABLE  1 7.  43 

EXPONENTIAL  FUNCTIONS. 

Values  of  e*  and  e~*  intermediate  to  those  here  given  may  be  found  by  adding  or  subtracting 
the  values  of  the  hyperbolic  cosine  and  sine  given  in  Tables  15  and  13. 


X 

logio(ea:) 

e* 

r- 

X 

logio(e') 

e* 

tr* 

0.0 

0.00000 

1.  0000 

I.OOOOOO 

5.0 

2.17147 

148.41 

0.006738 

.i 

•04343 

.1052 

0.904837 

.1 

.21490 

164.02 

.006097 

.2 

.08686 

.2214 

.818731 

.2 

.25833 

181.27 

•005517 

•3 

•  13^29 

•3499 

.740818 

•3 

.30176 

200.34 

.004992 

•4 

•17372 

.4918 

.670320 

.4 

221.41 

.004517 

0.5 

0.2^715 

1.6487 

0.606531 

5.5 

2.38862 

244.69 

0.004087 

.6 

.29058 

.8221 

.548812 

.6 

$3205 

270.43 

.003698 

.7 

.30401 

2.0138 

.496585 

•7 

•47548 

298.87 

.003346 

•9 

•34744 
.39087 

•2255 
•4596 

•449329 
•406570 

.8 
•9 

•$1891 
•56234 

330.30 
365-04 

.003028 
.002739 

1.0 

0.43429 

2.7183 

0.367879 

6.0 

2.60577 

403-43 

0.002479 

.i 

.47772 

3.0042 

•332871 

.1 

.64920 

445-86 

.002243 

.2 

.52115 

.3201 

.301194 

.2 

•69263 

492.75 

.002029 

•3 
•4 

:$p 

.6693 
4-0552 

•272532 
.246597 

•3 
•4 

.73606 
.77948 

544-57 
601.85 

.001836 
.001662 

1.5 

0.65144 

4-48i7 

0.223130 

6.5 

2.82291 

665.14 

0.001503 

.6 

.69487 

•953° 

.201897 

.6 

.86634 

735-10 

.001360 

•7 

.73830 

5-4739 

.182684 

•7 

.90977 

812.41 

.001231 

.8 
•9 

•78173 
.82516 

6.0496 
6.6859 

.165299 
.149569 

.8 
•9 

•95320 
.99663 

897.85 
992.27 

.001114 
.001008 

2.0 

0.86859 

7-3891 

0-135335 

7.0 

3.04006 

1096.6 

0.000912 

.i 

.91202 

8.1662 

.122456 

.1 

.08349 

J2I2.O 

.000825 

.2 

•95545 

9.0250 

.110803 

.2 

.12692 

13394 

.000747 

•3 

.99888 

9.9742 

.100259 

•3 

•17035 

1480.3 

.000676 

•4 

1.04231 

11.023 

.09071.8 

•4 

.21378 

1636.0 

.000611 

2.5 

1.08574 

12.182 

0.082085 

7.5 

3.25721 

1  808.0 

0.000553 

.6 

.12917 

13.464 

•074274 

.6 

.30064 

I998.2 

.000500 

•7 

.17260 

14.880 

.067206 

•7 

•34407 

2208.3 

•000453 

.8 

.21602 

16.445 

.060810 

.8 

•38750 

2440.6 

.000410 

•9 

•25945 

18.174 

•055023 

•9 

•43°93 

2697.3 

.000371 

30 

1.30288 

20.086 

0.049787 

80 

3-47436 

2981.0 

0.000335 

.i 

•34631 

22.198 

.045049 

.1 

.51779 

3294-5 

.000304 

.2 

•3 

•38974 
•433  i  7 

24-533 
27.113 

.040762 

.036883 

•  2 

•3 

.56121 
.60464 

3641.0 
4023.9 

.000275 
.000249 

•4 

.47660 

29.964 

•033373 

.4 

.64807 

4447-1 

.000225 

3.5 

1.52003 

33.115 

0.030197 

8.5 

3.69150 

4914.8 

0.000203 

.6 

•56346 

36.598 

.027324 

.6 

•73493 

543  '-7 

.000184 

.7 

.60689 

40.447 

.024724 

•7 

•77836 

6002.9 

.000167 

.8 

.65032 

44.701 

.022371 

.8 

.82179 

6634.2 

.000151 

•9 

•69375 

49.402 

.020242 

•9 

.86522 

7332.0 

.000136 

4.0 

.i 

I.737I8 
.78061 

54.598 
60.340 

0.018316 

•016573 

9.0 

.1 

3-90865 
.95208 

8103.1 

0.000123 

.000112 

.2 

.82404 

66.686 

.014996 

.2 

•995  5  * 

9897.1 

.000101 

•3 

.86747 

73-700 

.013569 

•3 

4.03894 

10938. 

.000091 

•4 

.91090 

81.451 

.012277 

•4 

.08237 

12088. 

.000083 

4.5 

1  -95433 

90.017 

0.011109 

9.5 

4.12580 

13360. 

0.000075 

.6 

•99775 

99.484 

.010052 

.6 

.16923 

14765- 

.000068 

•7 

2.04118 

109.95 

.009095 

•7 

.21266 

16318. 

.000061 

.8 

.08461 

121.51 

.008230 

.8 

.25609 

18034. 

.000055 

•9 

.12804 

134.29 

.007447 

•9 

.29952 

19930. 

.OOOO5O 

5.0 

2.17147 

148.41 

0.006738 

10.0 

4-34294 

22026. 

0.000045 

Taken  from  Glaisher's  '  Tables  of  the  Exponential  Function,'  Trans.  Cambridge  Phil.  Soc.  vol.  xiii.  1883.  This 
volume  also  contains  a  '  Table  of  the  Descending  Exponential  to  Twelve  or  Fourteen  Places  of  Decimals,'  by  F.  W. 
Newman. 

SMITHSONIAN  TABLES. 


44  TABLE  18. 

EXPONENTIAL  FUNCTIONS,  LOG  e*. 


X 

w 

X 

logIoM 

X 

>0g,o(,) 

X 

logrfO 

1  0.0 

4.34294 

15-0 

6.51442 

20.0 

8.68589 

25.0 

10.85736 

.1 

.38637 

.1 

.55785 

.1 

.72932 

.90079 

.2 

.42980 

.2 

.60128 

.2 

.77275 

.2 

.94422 

•3 

•47323 

•3 

.64471 

•3 

.8l6l8 

•3 

.98765 

•4 

.51666 

•4 

.68814 

•4 

•85961 

•4 

11.03108 

loi 

4.56009 
.60352 

I5i 

6.73*56 
-77499 

20.5 

8.90304 
.94647 

25-5 

11.07451 
.11794 

•7 

•64695 

•7 

.81842 

•7 

.98990 

•7 

.16137 

.8 
•9 

.69038 
•7338i 

.8 
-9 

.86185 
.90528 

.8 
•9 

9-03333 
.07675 

.8 
•9 

.20480 

.24823 

II.O 

4.77724 

1  6.0 

6.94871 

2I.O 

9.I2OI8 

26.0 

11.29166 

.1 

.82067 

.1 

.99214 

.1 

.l636l 

.1 

•33509 

.2 

.86410 

.2 

7.03557 

•2 

.20704 

.2 

•37852 

•3 

•90753 

•3 

.07900 

•3 

•25047 

•3 

.42194 

.4 

.95096 

•4 

.12243 

•4 

•29390 

'   -4 

.46537 

"•5 

4-99439 

16.5 

7.16586 

21.5 

9-33733 

26.5 

11.50880 

.6 

5.03782 

.6 

.20929 

.6 

.38076 

.6 

.55223 

•7 

.08125 

•7 

.25272 

•7 

.42419 

•7 

•59566 

.8 

.12467 

.8 

•29615 

.8 

.46762 

.8 

.63909 

•9 

.16810 

•9 

.33958 

•9 

.51105 

•9 

.68252 

I2.O 

5.21153 

17.0 

7-38301 

22.0 

9-55448 

27.0 

11.72595 

.1 

.25496 

.1 

.42644 

.1 

•59791 

.76938 

.2 

.29839 

.2 

.46987 

.2 

.64134 

.2 

.81281 

•3 

.4 

.34182 
•38525 

•3 

•4 

•51329 
•55672 

•3 

•4 

•68477 
.72820 

•3 
•4 

.85624 
.89967 

12.5 

5.42868 

J7-5 

7.60015 

22.5 

9.77163 

27-5 

11.94310 

.6 

.47211 

.6 

•64358 

.6 

.8  1  506 

.6 

•98653 

•7 

•51554 

•7 

.68701 

•7 

.85848 

•7 

12.02996 

.8 

•55897 

.8 

•73044 

.8 

.90191 

.8 

•07339 

•9 

.60240 

•9 

•77387 

•9 

•94534 

•9 

.11682 

13.0 

5.64583 

18.0 

7.81730 

23.0 

9.98877 

28.0 

12.16025 

.1 

.68926 

.1 

.86073 

.1 

10.03220 

.1 

.20367 

.2 

.73269 

.2 

.90416 

.2 

•07563 

.2 

.24710 

•3 

.77612 

•3 

•94759 

•3 

.11906 

•3 

.29053 

•4 

•8i955 

•4 

.99102 

•4 

.16249 

•4 

.33396 

13.5 

5.86298 

18.5 

8-03445 

23-5 

10.20592 

28.5 

12.37739 

.6 

.90640 

.6 

.07788 

.6 

•24935 

.6 

.42082 

3 

.94983 
5-99326 

i 

.12131 

.16474 

1 

.29278 
•  -33621 

.8 

.46425 
.50768 

•9 

6.03669 

•9 

.20817 

•9 

•37964 

•9 

•55111 

14.0 

6.08012 

19.0 

8.25160 

24.0 

10.42307 

29.0 

12.59454 

.1 

•J2355 

.1 

.29502, 

.1 

.46650 

.1 

.63797 

.2 

.16698 

.2 

•33845 

.2 

•5°993 

.2 

.68140 

•3 

.21041 

•3 

.38188 

•3 

•55336 

•3 

.72483 

•4 

•25384 

•4 

•42531 

-4 

•59679 

•4 

.76826 

14-5 

6.29727 
.34070 

<9;5 

8.46874 
.51217 

24:I 

10.64021 
.68364 

29:l 

12.81169 
.85512 

.7 

•38413 

.7 

•5556o 

.7 

•72707 

•7 

.89855 

.8 

•42756 

.8 

•59903 

.8 

•77050 

.8 

.94198 

•9 

•47099 

•9 

.64246 

•9 

•9 

.98541 

15.0 

6.51442 

2O.O 

8.68589 

25.0 

10.85736 

30.0 

13.02883 

SMITHSONIAN  TABLES. 


TABLE  19. 
EXPONENTIAL  FUNCTIONS. 

Value  of  e*a  and  e-«3  and  their  logarithms. 


45 


The  equation  to  the  probability  curve  is  y  =. , 
negative,  between  zero  and  infinity. 


*a,  where  x  may  have  any  value,  positive  or 


* 

^ 

log  ex* 

r* 

log  e-J? 

0.1 

I.OIOI 

0.00434 

0.99005 

1.99566 

2 

1.0408 

01737 

96079 

98263 

3 

.0904 

03909 

9*393 

96091 

4 

•1735 

06949 

85214 

93051 

5 

.2840 

10857 

77880 

89*43 

0.6 

-4333 

0.15635 

0.69768 

1.84365 

7 

21280 

61263 

78720 

8 

.8965 

27795 

52729 

72205 

9 

2.2479 

35178 

44486 

64822 

I.O 

2-7183 

43429  . 

36788 

56571 

1.1 

3-3535 

0.52550 

0.29820 

1.47450 

2 

4.2207 

62538 

2:3693 

37462 

3 

5-4I95 

73396 

18452 

26604 

4 

7.0993 

85122 

14086 

14878 

5 

9.4877 

97716 

10540 

02284 

1.6 

1.2936  X  io 

1.  11179 

0.77306  X  io-1 

2.88821 

7 

1-7993 

255*1 

55576   " 

74489 

8 

2-5534   " 

40711 

39*64   " 

59289 

9 

3.6996   " 

56780 

27052 

43220 

2.0 

54598   " 

18316   " 

26282 

2.1 

8.2269   " 

1.91524 

0.12155   " 

2.08476 

2 

1.2647  X  io2 

2.10199 

79070  X  io-2 

3^89801 

3 

1.9834   « 

29742 

50418 

70258 

4 

5OI54 

3*5** 

49846 

5 

5.1802   " 

7*434 

19304 

28566 

2.6 

7 

8.6264   " 
i.  4656  X  io3 

2.93583 
3.16601 

0.11592   " 

68233  X  10-3 

3.06417 
4.83400 

8 

2.5402   " 

40487 

39367    " 

595*3 

9 

4.4918   " 

65242 

22263    " 

34758 

3-° 

8.1031   « 

90865 

I234I 

09*35 

3.1 

1.4913  X  io4 

4-17357 

0.67055  X  io~4 

5.82643 

2 

3 

2.8001   " 
5-3638   " 

447*8 
72947 

357*3 
18644 

55283 
27053 

4 

1.0482  X  io5 

5-02044 

95402  X  io~5 

6.97956 

5 

2.0898   " 

32011 

47851   •« 

67989 

3.6 

4-2507   " 

5.62846 

0.23526   " 

6-37*54 

8 

8.8205   " 
1.8673  X  io« 

94549 
6.27121 

1*337   " 
53554  X  io-« 

0545* 
7.72879 

9 

4.0329   " 

60562 

24796 

39438 

4.0 

8.8861   " 

94871 

11254 

05129 

4.1 

1.9976  X  io7 

7.30049 

0.50062  X  io~7 

5.69951 

2 

4.5809   " 

66095 

21829   " 

33905 

3 

1.0718  X  io8 

8.03011 

93303  X  IO-8 

9.96989 

4 

2.5583 

40796 

39088  « 

59204 

5 

6.2297 

79447 

16052   " 

20553 

4.6 

1.5476  X  io9 

9.18967 

0.64614  X  io-* 

10.81033 

§ 

3.9228   " 
1.0143  X  io10 

59357 
10.00615 

25494 
98595  X  10-10 

40643 
II-99385 

9 

2.6755   " 

42741 

37376   " 

57259 

S-o 

7.2005   « 

85736 

v  i  3888   " 

14264 

SMITHSONIAN  TABLES. 


46 


TABLE  20. 
EXPONENTIAL   FUNCTIONS. 

w  vf 

Values  ol  0**  and 6     *   and  their  logarithms. 


X 

rr 
0** 

log  8** 

IT 

e~^* 

log*"** 

1 

2-1933 

0.34109 

0.45594 

1.65891 

2 

4.8105 

.68219 

.20788 

.31781 

3 

1.0551  X  10 

1.02328 

.94780  X  io-1 

2.97672 

4 

2.3141 

-36438 

.43214 

.63562 

5 

5-0754 

•70547 

.19703 

•29453 

6 

1.1132  X  io2 

2.04656 

0.89833  X  10-2 

3-95344 

7 

2.4415   " 

.38766 

.40958  « 

.61234 

8 

5-3549   " 

-72875 

.18674  " 

.27125 

9 

1.1745  X  io3 

3.06985 

.85144  X  IO-3 

4-930I5 

10 

2.5760   « 

.41094 

.38820   " 

.58906 

11 

12 

5.6498   « 
1.2392  X  io* 

3-75204 
4-093!3 

0.17700   " 
.80699  X  io~4 

4.24796 
5.90687 

13 

2.7168   " 

.43422 

.36794   " 

.56578 

14 
15 

5.9610   " 
1.3074  X  io5 

•77532 
5.11641 

.16776  •' 

.76487  X  io~5 

.22468 
6.88359 

16 

2.8675   " 

5-45751 

0.34873  " 

6.54249 

17 

6.2893   « 

.79860 

.15900  '• 

.20140 

18 

1-3794  X  io6 

6.13969 

.72495  X  I0~6 

7.86031 

!9 
20 

3-0254 
6.6356   « 

.48079 
.82189 

•33053 
.15070 

.51921 
.17812 

TABLE  21 . 
EXPONENTIAL  FUNCTIONS. 


Values  of  0  <•  *  and 


and  their  logarithms. 


X 

e~r" 

,g^ 

r* 

"& 

1 

'•5576 

0.19244 

0.64203 

1.80756 

2 

2.4260 

.38488 

.41221 

.61512 

3 

3.7786 

•57733 

.26465 

.42267 

4 

5-8853 

•76977 

.16992 

.23023 

5 

9.1666 

.96221 

.10909 

•03779 

6 

14.277 

1.15465 

0.070041 

2.84535 

7 

22.238 

•34709 

.044968 

.65291 

8 

34-636 

•53953 

.028871 

.46047 

9 

53-948 

•73198 

.018536 

.26802 

IO 

84.027 

.92442 

.011901 

•07558 

11 

130.87 

2.11686 

0.0076408 

3.88314 

12 

203.85 

.30930 
.50174 

.0049057 
.0031496 

.69070 
.49826 

14 

494.52 

.69418 

.OO2O222 

.30582 

15 

770.24 

.88663 

.0012983 

•IJ337 

16 

1199.7 

3.07907 

0.00083355 

4.92093 

I7 

1868.5 

.27151 

.00053517 

.72849 

18 

2910.4 

•46395 

.00034360 

•53605 

19 

4533-1 

.00022060 

20 

7060.5 

*4 

.00014163 

.15117 

SMITHSONIAN  TABLES. 


TABLES  22  AND  23.    EXPONENTIAL  FUNCTIONS  AND  LEAST  SQUARES.    47 

TABLE 22.  —Exponential  Functions. 
Value  of  e*  and  e~*  and  their  logarithms. 


X 

<* 

log** 

,- 

X 

e* 

log<?* 

.,- 

i/64 

1.0157 

0.00679 

0.98450 

i/3 

I-3956 

0.14476 

0-71653 

1/32 

.0317 

.01357 

.96923 

1/2 

.6487 

.21715 

.60653 

i/i6 

.0645 

.02714 

•93941 

3/4 

2.1170 

•32572 

.47237 

I/IO 

.1052 

.04343 

.90484 

i 

•7183 

.43429 

.36788 

J/9 

."75 

.04825 

.89484 

5/4 

3-4903 

•54287 

.28650 

1/8 

1.1331 

0.05429 

0.88250 

3/2 

4.4817 

0.65144 

0.22313 

1/7 

.1536 

.06204 

.86688 

7/4 

5-7546 

.76002 

•I7377 

1/6 

.1814 

.07238 

.84648 

2 

7.3891 

.86859 

1/5 

.2214 

.08686 

.81873 

9/4 

9.4877 

.97716 

.10540 

1/4 

.2840 

.10857 

.77880 

5/2 

12.1825 

1.08574 

.08208 

TABLE  23.  —Least  Squares. 
Values  of  P  =  - 


This  table  gives  the  value  of  P,  the  probability  of  an  observational  error  having  a  value  posi- 
tive or  negative  equal  to  or  less  than  x  when  h  is  the  measure  of  precision,  P  =  —   T      f-<hx) 

\ir*J  O 

d(hx},     For  values  of  the  inverse  function  see  the  table  on  Diffusion. 


kx 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

0.0 

.01128 

.02256 

•03384 

.04511 

•05637 

.06762 

.07886 

.09008 

.10128 

.11246 

.1 

.12362 

•13476 

•14587 

•^695 

.16800 

.17901 

.18999 

.20094 

.21184 

.22270 

.2 

•23352 

.24430 

.25502 

•26570 

•27633 

.28690 

.29742 

.30788 

.31828 

•32863 

•3 

•33891 

•349  i  3 

•35928 

•36936 

•37938 

•38933 

.39921 

.40901 

.41874 

•42839 

•4 

•43797 

•44747 

•45689 

.46623 

•47548 

.48466 

•49375 

•50275 

.51167 

•52050 

0.5 

.6 

.52924 
.61168 

•5379° 
.61941 

.54646 
•62705 

•55494 
•63459 

•56332 
.64203 

.57162 
.64938 

.57982 
.65663 

•58792 
•66378 

•59594 
.67084 

.60386 
.67780 

.7 

.68467 

.69143 

.69810 

.70468 

.71116 

•71754 

•72382 

•73001 

.73610 

.74210 

.8 

.74800 

.75952 

.76514 

.77067 

.77610 

.78144 

.78669 

.79184 

.79691 

•9 

.80188 

.80677 

.81156 

.81627 

.82089 

.82542 

.82987 

•83423 

.83851 

.84270 

1.0 

.84681 

.85084 

.85478 

.85865 

.86244 

.86614 

.86977 

•87333 

.87680 

.88021 

.i 

•88353 

.88679 

.88997 

.89308 

.89612 

.89910 

.90200 

.90484 

.90761 

.91031 

.2 

.91296 

•9I553 

.91805 

•92051 

.92290 

•92524 

•9275! 

•92973 

.93190 

.93401 

•3 

.93606 

.93807 

.94002 

.94191 

•94376 

•94556 

•947  3  i 

.94902 

•95067 

•95229 

•4 

•95385 

•95538 

.95686 

•95830 

•95970 

.96105 

•96237 

•96365 

.96490 

.96611 

1.5 

.96728 

.96841 

•96952 

•97059 

.97162 

.97263 

•97360 

•97455 

•97546 

•97635 

.6 

.97721 

.97804 

.97884 

.97962 

.98038 

.98110 

.98181 

.98249 

•98315 

•98379 

•7 

.98441 

.98500 

•98558 

•98613 

.98667 

.98719 

.98769 

.98817 

.98864 

.98909 

.8 
•9 

•98952 
.99309 

•98994 
•9933s 

•99035 
•99366 

•99074 
•99392 

.99111 
.99418 

.99147 
•99443 

•99182 
.99466 

.99216 
.99489 

.99248 
•995  " 

.99279 
•99532 

2.0 

•99552 

•99572 

•99591 

.99609 

.99626 

.99642 

.99658 

•99673 

.90688 

.99702 

.1 

•99715 

.99728 

.99741 

•99753 

.99764 

•99775 

•99785 

•99795 

•99805 

.99814 

.2 

.99822 

.99831 

.99839 

.99846 

.99854 

.99861 

.99867 

.99874 

.99880 

.99886 

•3 

.99891 

•99897 

.99902 

.99906 

.9991  1 

.99920 

•99924 

.99928 

•9993  i 

•4 

•99935 

•99938 

.99941 

•99944 

•99947 

.99950 

•99952 

•99955 

•99957 

•99959 

2.5 

.99961 

.99963 

.99965 

•99967 

•99969 

.99971 

•99972 

•99974 

•99975 

.99976 

.6 

•99978 

•99979 

.99980 

.99981 

.99982 

.99983 

.99984 

•99985 

.99986 

•99987 

•7 

•99987 

.99988 

•99989 

•99989 

•99990 

.99991 

.99991 

.99992 

•99992 

•99992 

.8 

•99993 

•99993 

•99994 

•99994 

•99994 

•99995 

•99995 

•99995 

•99996 

•99996 

•9 

•99996 

.99996 

•99997 

•99997 

•99997 

•99997 

•99997 

.99997 

•99998 

•99998 

3.0 

-99999 

•99999 

I.OOOOO 

Taken  from  a  paper  by  Dr.  James  Burgess  '  on  the  Definite  Integral  JL  f*  er-&  dty  with  Ex- 

•y  7JY/    O 

tended  Tables  of  Values.'     Trans.  Roy.  Soc.  of  Edinburgh,  vol.  xxxix,  1900,  p.  257. 
SMITHSONIAN  TABLES. 


48  TABLE  24. 

LEAST  SQUARES. 

This  table  gives  the  values  of  the  probability  P,  as  defined  in  last  table,  corresponding  to  different  values  of 
x I  r  where  r  is  the  "  probable  error."     The  probable  error  r  is  equal  to  0.476947  Jt. 


an 
r 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

0.0 

.00000 

.00538 

.01076 

.01614 

.02152 

.02690 

.03228 

.03766 

•04303 

.04840 

O.I 

•05378 

.05914 

.06451 

.06987 

•07523 

.08059 

•08594 

.09129 

.09663 

.10197 

O.2 

.10731 

.11264 

.11796 

.12328 

.12860 

I339I 

.13921 

•I4451 

.14980 

•  15508 

o-3 

.16035 

.16562 

.17088 

.17614 

.18138 

.18662 

.19185 

.19707 

.20229 

.20749 

0.4 

.21268 

.21787 

.22304 

.22821 

.23336 

.23851 

.24364 

.24876 

•25388 

.25898 

0.5 

.26407 

.26915 

.27421 

.27927 

.28431 

.28934 

.29436 

•29936 

•30435 

•30933 

0.6 

•3H30 

•31925 

.32419 

.32911 

•33402 

•33892 

.34380 

.34866 

•35352 

•35835 

0.7 

•363  i  7 

.36798 

•37277 

•37755 

•38231 

.38705 

•39*78 

•39649 

.40118 

.40586 

0.8 

.41052 

•4i5r7 

.41979 

.42440 

.42899 

•43357 

•43813 

.44267 

.44719 

.45169 

0.9 

.45618 

.46064 

.46509 

.46952 

•47393 

.47832 

.48270 

48605 

•49139 

•49570 

1.0 

i.i 

.50000 
.54188 

.50428 
•54595 

•50853 
.55001 

•5I277 
.55404 

.51699 
.55806 

.52119 
.56205 

•52537 
.56602 

•52952 
•  56998 

•53366 
•57391 

•53778 
•57782 

1.2 

.58171 

•58558 

•58942 

•59325 

•59705 

.60083 

.60460 

•60833 

.61205 

•6i575 

i-3 

.61942 

.62308 

.62671 

.63032 

.63391 

•63747 

.64102 

•64554 

.64804 

•65152 

1.4 

.65498 

.65841 

.66182 

.66521 

.66858 

•67193 

.67526 

•67856 

.68184 

.68510 

1.5 

.68833 

•691  55 

.69474 

.69791 

.70106 

.70419 

.70729 

.71038 

.71344 

.71648 

1.6 

.71949 

.72249 

•72546 

.7284! 

•73134 

•73425 

.73714 

.74000 

.74285 

•74567 

i-7 

.74847 

•75I24 

.75400 

•75674 

•75945 

.76214 

.76481 

.76746 

.77009 

.77270 

1.8 

.77528 

•77785 

.78039 

.78291 

•78542 

.78790 

.79036 

.79280 

•79522 

.79761 

1.9 

•79999 

•80235 

.80469 

.80700 

.80930 

.81158 

•81383 

.81607 

.81828 

.82048 

2.0 

.82266 

.82481 

.82695 

.82907 

.83117 

•83324 

•83530 

•83734 

•83936 

•84137 

2.1 

2.2 

•84335 
.86216 

•84531 
.86394 

.84726 
.86570 

.84919 
.86745 

.85109 
.86917 

.85298 
.87088 

.85486 
.87258 

.85671 
•87425 

.85854 
•87591 

.86036 
•87755 

2-3 

.87918 

.88078 

.88237 

•88395 

•88550 

.88705 

.88857 

.89008 

.89157 

.89304 

2.4 

.89450 

•89595 

.89738 

.89879 

.90019 

•90157 

•90293 

.90428 

.90562 

.90694 

2.5 

.90825 

.90954 

.91082 

.91208 

•9J332 

.91456 

•9*578 

.91698 

.91817 

•91935 

2.6 

.92051 

.92166 

.92280 

.92392 

•92503 

.92617 

.92721 

.92828 

•92934 

•93038 

2.7 

•93I4I 

•93243 

•93344 

•93443 

•93541 

•93638 

•93734 

.93828 

.93922 

.94014 

2.8 

.94105 

•94195 

.94284 

•94371 

•94458 

•94543 

.94627 

.94711 

•94793 

.94874 

2.9 

•94954 

•95033 

.95111 

•95187 

•95263 

•95338 

.95412 

•95484 

•95557 

.95628 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

3 

.95698 

.96346 

.96910 

•97397 

.97817 

.98176 

.98482 

•98743 

.98962 

.99147 

4 

.99302 

•99431 

•99539 

99627 

.99700 

.99760 

.99808 

.99848 

•99879 

.99905 

5 

.99926 

•99943 

.99956 

.99966 

•99974 

.99980 

•99985 

.99988 

.99991 

•99993 

TABLE  25. 
LEAST  SQUARES. 

Values  of  the  factor  o.6745\/-^r . 

\»»— 1 

This  factor  occurs  in  the  equation  *   =r  o.6j4S\   —   for  tne  probable  error  of  a  single  observation,  and  other 

j|  n — i 
similar  equations. 


n   = 

1 

2 

3 

4 

5 

6 

7 

8 

9 

00 

0-6745 

0.4769 

0.3894 

0.3372 

0.3016 

0.2754 

0.2549 

0.2385 

10 

20 

0.2248 
•1547 

0.2133 
.1508 

.2029 
.1472 

.1947 
•1438 

.1871 
.1406 

.1803 
•1377 

.1742 
•1349 

.1686 
•!323 

.1636 
.1298 

.1590 
•1275 

3° 

.1252 

.1231 

.1211 

.1192 

.1174 

."57 

.1140 

.1124 

.1109 

.1094 

40 

.1080 

.1066 

•1053 

.1041 

.1029 

.1017 

.1005 

.0994 

.0984 

.0974 

50 

0.0964 

0.0954 

0.0944 

0.0935 

0.0926 

0.0918 

0.0909 

0.0901 

0.0893 

0.0886 

60 

.0878 

.0871 

.0864 

.0857 

.0850 

.0843 

.0837 

.0830 

.0824 

.0818 

70 

.0812 

.0806 

.0800 

•0795 

.0789 

.0784 

•0778 

•0773 

.0768 

.0763 

80 
90 

•0759 
•0715 

•0754 
.0711 

.0749 
.0707 

•0745 
.0703 

.0740 
.0699 

.0736 
.0696 

•0731 
.0692 

.0727 
.0688 

.0723 
.0685 

,0719 
.0681 

SMITHSONIAN  TABLES. 


TABLE  26. 
LEAST  SQUARES 

Values  of  the  factor  0.6745 


49 


_--. 


This  factor  occurs  in  the  equation  e    =  o.6j4$\      ^     for  the  probable  error  of  the  arithmetic  mean. 

\  n(n — i) 


»   = 

1 

*2 

3 

4 

5 

6 

7 

8 

9 

00 

10 

0.0711 

0.0643 

0.4769 
.0587 

0.2754 
.0540 

0.1947 
.0500 

0.1508 
.0465 

0.1231 
•0435 

0.1041 
.0409 

0.0901 
.0386 

0.0795 
•0365 

20 

.0346 

.0329 

.0314 

.0300 

.0287 

.0275 

.0265 

.0255 

.0245 

.0237 

30 

0.0229 

0.0221 

0.0214 

0.0208 

0.0201 

0.0196 

0.0190 

0.0185 

0.0180 

0.0175 

40 

.0171 

.0167 

.0163 

.0159 

•0155 

.0152 

.0148 

.0145 

.0142 

.0139 

50 

.0136 

.0134 

.0131 

.0128 

.OI26 

.0124 

.0122 

.0119 

.0117 

.0115 

TABLE  27. 
LEAST  SQUARES. 

Values  of  the  factor  0.8453-v/     * 


This  factor  occurs  in  the  equation  et  =  0.8453 


for  the  probable  error  of  a  single  observation. 


n   - 

1 

2 

3 

4 

5 

6 

7 

8 

9 

00 

10 

0.0891 

0.0806 

0.5978 
.0736 

o.345i 
.0677 

0.2440 
.0627 

0.1890 
•°583 

o.i543 
.0546 

0.1304 
•0513 

0.1130 
.0483 

0.0996 

•0457 

20 

•0434 

.0412 

•0393 

.0376 

.0360 

•0345 

•0332 

.0319 

.0307 

.0297 

30 

0.0287 

0.0277 

0.0268 

0.0260 

0.0252 

0.0245 

0.0238 

0.0232 

0.0225 

0.0220 

40 

.0214 

.0209 

.0204 

.0199 

.0194 

.0190 

.0186 

.0182 

.0178 

.0174 

50 

.0171 

.0167 

.0164 

.0161 

.0158 

.0155 

.0152 

.0150 

.0147 

.0145 

TABLE  28. 
LEAST  SQUARES, 


Values  of  0.8453^ 

This  table  gives  the  average  error  of  the  arithmetic  mean  when  the  probable  error  is  one. 


n   = 

1 

2 

3 

4 

5 

6 

7 

8 

9 

00 

0.4227 

0.1993 

0.1220 

0.0845 

0.0630 

0.0493 

0.0399 

0.0332 

10 

20 

0.0282 
.0097 

0.0243 
.0090 

.0212 
.0084 

.0188 
.0078 

.0167 
.0073 

.0151 
.0069 

.0136 
.0065 

.0124 
.0061 

.0114 
.0058 

.0105 
•0055 

30 

0.0052 

0.0050 

0.0047 

0.0045 

0.0043 

0.0041 

0.0040 

0.0038 

0.0037 

0.0035 

40 

.0034 

•0033 

.0031 

.0030 

.OO29 

.0028 

.0027 

.0027 

.0026 

.0025 

50 

.0024 

.0023 

.0023 

.0022 

.OO22 

.0021 

.0020 

.0020 

.0019 

.0019 

SMITHSONIAN  TABLES. 


50  TABLE  29. 

DIFFUSION. 

2     /-«  C&  da. 
Inverse*  values  of  v  fc  =  i  —  ^f~J0 

log  x  =  log  (2?)  +  log\//£A    t  expressed  in  seconds. 
=  log  8  +  \og\/ki.    t  expressed  in  days. 
=  log  7  -f-  log  \/kt.  "         "  years. 

j,    k  =  coefficient  of  diffusion.! 
*•  =  initial  concentration. 
v  =  concentration  at  distance  x,  time  t. 


V/C 

log  2? 

zq 

log  3 

1 

logy 

y 

0.00 

+  00 

+  00 

+  00 

+  00 

oo 

00 

.01 

0.56143 

3.6428 

3.02970 

1070.78 

4.31098 

20463. 

.02 

.51719 

3.2900 

2.98545 

967.04 

.26674 

18481. 

•03 

.48699 

3.0690 

.95525 

902.90 

•23654 

17240. 

.04 

.46306 

2.9044 

.93132 

853-73 

.2I26l 

16316. 

0.05 

0.44276 

2.7718 

2.91102 

814.74 

4.19231 

I557I- 

.06 

.07 

.42486 

.40865 

2.6598 

2.5624 

.89311 
.87691 

781.83 

753-20 

.17440 
.15820 

14942. 
H395- 

.08 

.39372 

2.4758 

.86198 

72775 

•14327 

13908. 

.09 

•37979 

2.3977 

.84804 

704.76 

•12933 

13469. 

0.10 

.11 

0.36664 
.35414 

2.3262 

2.2602 

2-83490 
.82240 

683.75 
664.36 

4.11619 
.10369 

13067. 
12697. 

.12 

.34218 

2.1988 

.81044 

646.31 

.09173 

12352. 

•13 

•33067 

2.1413 

•79893 

629.40 

.08022 

12029. 

.14 

•31954 

2.0871 

.78780 

613-47 

.06909 

11724. 

0.15 

0.30874 

2.0358 

2.77699 

598.40 

4.05828 

11436. 

.16 

.29821 

1.9871 

•76647 

584.08 

.04776 

11162. 

.17 

.28793 

1.9406 

•75619 

570.41 

.03748 

10901. 

.18 

.27786 

1.8961 

.74612 

557-34 

.02741 

10652. 

.19 

.26798 

1.8534 

.73624 

544.80 

•01753 

10412. 

0.20 

.21 

0.25825 
.24866 

1.8124 

1.7728 

2.72651 
.71692 

532.73 
521.10 

4.00780 
3.99821 

10181. 
9958.9 

.22 

.23919 

1-7346 

.70745 

509.86 

.98874 

9744.1 

•23 

.22983 

1.6976 

.69808 

498.98 

•97937 

9536.2 

.24 

.22055 

1.6617 

.68880 

488.43 

.97010 

9334-6 

0.25 

0.21134 

1.6268 

2.67960 

478.19 

3.96089 

9138.9 

.26 

.20220 

I-593° 

.67046 

468.23 

•95T75 

8948.5 

.27 

.19312 

1.5600 

•66137 

458-53 

.94266 

8763.2 

.28 

.18407 

1.5278 

.65232 

449.08 

.93361 

8582.5 

.29 

•17505 

1.4964 

.64331 

439-85 

.92460 

8406.2 

0.30 

0.16606 

1-4657 

2.63431 

430.84 

3.91560 

8233.9 

•32 

.15708 
.14810 

1-4357 
1.4064 

•62533 
.61636 

422.02 
4I3-39 

[89765 

8065.4 
7900.4 

•33 

.13912 

1.3776 

.60738 

404-93 

.88867 

7738.8 

•34 

.13014 

1-3494 

.59840 

396.64 

.87969 

7580.3 

0.35 

0.12114 

1.3217 

2.58939 

388.50 

3.87068 

7424.8 

•36 

.11211 

1.2945 

.58037 

380-51 

.86166 

7272.0 

•10305 

1.2678 

•57I3I 

372.66 

.85260 

7122.0 

.38 

.09396 

1.2415 

.56222 

364-93 

.84351 

6974.4 

•39 

.08482 

1.2157 

•55308 

357-34 

.83437 

6829.2 

0.40 

0.07563 

1.1902 

2.54389 

349-86 

3.82518 

6686.2 

.41 

.06639 

1.1652 

.53464 

342.49 

•8i593 

6545-4 

.42 

.05708 

1.1405 

•52533 

335-22 

.80662 

6406.6 

•43 

.04770 

1.1161 

.5T595 

328.06 

•79724 

6269.7 

•44 

.03824 

1.0920 

.50650 

320.99 

.78779 

6134.6 

0.45 

0.02870 

1.0683 

2.49696 

314.02 

3-77825 

6001.3 

.46 

.01907 

1.0449 

48733 

307-13 

.76862 

5869.7 

•47 

.00934 

1.0217 

.47760 

.75889 

5739-7 

.48 

9-9995  1' 

0.99886 

•46776 

293.60 

•749°5 

5611.2 

49 

.98956 

0.97624 

.45782 

286.96 

•73911 

5484.1 

0.50 

9-97949 

0.95387 

2-44775 

280.38 

3.72904 

5358.4 

*  Kelvin,  Mathematical  and  Physical  Papers,  vol.  III.  p.  428  ;  Becker,  Am.  Jour, 
of  Sci.  vol.  III.  1897,  p.  280.  t  For  direct  values  see  table  23. 

Taken  from  unpublished  manuscript  of  C.  E.  Van  Orstrand. 
SMITHSONIAN  TABLES, 


TABLE  29  (continued). 
DIFFUSION. 


v/c 

log  zq 

tq 

,OgJ 

S 

logy 

y 

0.50 

9-97949 

0.95387 

2.44775 

280.38 

3.72904 

5358.4 

.51 

.96929 

.93J74 

•43755 

273-87 

.71884 

5234.1 

.52 
•53 

.95896 
.94848 

.90983 
.88813 

.42722 
.41674 

267.43 
261.06 

.70851 
.69803 

5111.0 
4989.1 

•54 

.93784 

.86665 

.40610 

25474 

•68739 

4868.4 

0.55 

•56 

9.92704 
.91607 

0.84536 
.82426 

2-3953° 
•38432 

248.48 
242.28 

3-67659 
.66561 

4748.9 
4630.3 

•57 

.90490 

•80335 

236.13 

•65445 

4512.8 

•58 

.89354 

.78260 

.36180 

230.04 

.64309 

4396.3 

•59 

.88197 

.76203 

•35023 

223.99 

.63152 

4280.7 

0.60 

9.87018 

0.74161 

2.33843 

217.99 

3-6I973 

4166.1 

.61 

.85815 

•72135 

.32640 

212.03 

.60770 

4052.2 

.62 

.84587 

.70124 

.31412 

206.12 

•59541 

3939-2 

•63 

•83332 

.68126 

•3OI57 

200.25 

.58286 

3827.0 

.64 

.82048 

.66143 

.28874 

194.42 

•57003 

3715.6 

0.65 

.66 
•67 

9.80734 
.79388 
.78008 

0.64172 
.62213 
.60266 

2.27560 
.26214 
•24833 

188.63 
182.87 
177.15 

3.55689 

•54343 
.52962 

3604-9 
3494-9 
3385.4 

.68 

•76590 

•58331 

.23416 

171.46 

3276.8 

.69 

•75133 

.56407 

.21959 

165.80 

.50088 

3168.7 

0.70 

.72 

973634 

.72089 

•70495 

n 

2.20459 
.18915 
.17321 

160.17 
154.58 
149.01 

3.48588 
.47044 
4545° 

3061.1 
2954.2 
2847.7 

•73 

.68849 

.48808 

.15675 

143-47 

•43804 

2741.8 

•74 

.67146 

.46931 

.13972 

'37-95 

.42101 

2636.4 

0.75 

9.65381 

0.45062 

2.12207 

132.46 

3-40336 

253*4 

•76 

•63550 

.43202 

.10376 

126.99 

•38505 

2426.9 

•77 

.61646 

.41348 

.08471 

121.54 

.36600 

2322.7 

•78 

.59662 

.39502 

.06487 

n6.ii 

.34616 

2219.0 

•79 

•57590 

.37662 

.04416 

110.70 

.32545 

2115.7 

0.80 

9.55423 

0.35829 

2.02249 

105-31 

3-30378 

2012.7 

,8  1 

•5315° 

.34001 

1.99975 

99-943 

.28104 

1910.0 

.82 

.50758 

.32180 

•97584 

94-589 

•25713 

1807.7 

•83 
.84 

•48235 
•45564 

.30363 

.28552 

.95061 
•92389 

89.250 
83.926 

.23190 
.20518 

1705-7 
1603.9 

0.85 

9.42725 

0.26745 

I-8955I 

78.615 

3.17680 

1502.4 

.86 
.87 

•39695 
•36445 

.24943 
.23145 

.86521 
.83271 

73-3!7 
68.032 

.14650 
.11400 

1401.2 
1300.2 

.88 

•32940 

.21350 

.79766 

62.757 

.07895 

1199.4 

.89 

•29135 

.19559 

.7596i 

57492 

3-04090 

1098.7 

0.90 

.91 

9.24972 

•20374 

0.17771 
.15986 

1.71797 
.67200 

52.236 
46.989 

2.99926 
•95329 

99|3i 

.92 

•15239 

.14203 

.62065 

4I-750 

.90194 

797.89 

•93 

.09423 

.12423 

.56249 

36-516 

•84378 

697-88 

•94 

9.02714 

.10645 

•49539 

31.289 

.77668 

597-98 

0.95 

8.94783 

0.08868 

1.41609 

26.067 

2.69738 

498.17 

.96 

.85082 

.07093 

.31907 

20.848 

.60036 

398.44 

•97 

.72580 

.05319 

.19406 

15.633 

•47535 

298.78 

•98 

•54965 

.03545 

.01791 

10.421 

.29920 

199.16 

•99 

.24859 

.01773 

9.71684 

5.21007 

1.99813 

99-571 

1.00 

—  00 

o.ooooo 

—  oo 

o.ooooo 

—  00 

0.000 

SMITHSONIAN  TABLES. 


TABLE  30. 
GAMMA  FUNCTION.* 


Value  of  log  I     e—af^dx  + 10. 

Jo 

Values  of  the  logarithms  + 10  of  the  "  Second  Eulerian  Integral "  (Gamma  function)    |     e-*x*-*dx  or  log  T(n )4-ro 

Jo 

for  values  of  n  between  i  and  2.    When  n  has  values  not  lying  between  i  and  2  the  value  of  the  function  can  be 
readily  calculated  from  the  equation  r(»+i)  =  nT(n)  =.  «(»— i)  .  .  .  («— r)T(n— r). 


r 

Jo 


n 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

1.00 

9>99  

97497 

95ooi 

92512 

90030 

87555 

85087 

82627 

80173 

77727 

I.OI 
1.02 

75287 
51279 

4891! 

70430 
46561 

68011 
44212 

65600 

41870 

63196 
39535 

60799 
37207 

58408 
34886 

56025 

32572 

53648 
30265 

1.03 
1.04 

27964 
05334 

25671 
03108 

23384 

21104 
98677 

18831 
96471 

16564 
94273 

9^ 

1  2052 
89895 

09806 
87716 

07567 
85544 

1.05 

9-9883379 

81220 

79068 

76922 

74783 

72651 

70525 

68406 

66294 

64188 

i.  06 

62089 

59996 

579*0 

55830 

53757 

51690 

49630 

47577 

45530 

43489 

1.07 

41469 

39428 

37407 

35392 

33384 

31382 

29387 

27398 

25415 

23449 

i.  08 
1.09 

21469 
02123 

19506 
00223 

17549 
98329 

15599 
96442 

13655 
9456i 

11717 
92685 

07860 
89856 

05941 
87100 

04025 
3-5250 

1.10 

9.9783407 

81570 

79738 

779*4 

76095 

74283 

72476 

70676 

68882 

67095 

i.  ii 

65313 

63538 

61768 

60005 

58248 

56497 

54753 

53014 

51281 

49555 

1.  12 

47834 

46120 

44411 

42709 

41013 

39323 

37638 

34288 

32622 

I.I3 

30962 

29308 

27659 

26017 

24381 

22751 

21126 

19508 

17896 

16289 

I.I4 

14689 

13094 

11505 

09922 

08345 

06774 

05209 

03650 

02096 

00549 

1.15 

9.9699007 

97471 

95941 

94417 

92898 

91386 

89879 

88378 

86883 

85393 

1.16 

83910 

82432 

80960 

79493 

78033 

76578 

75I29 

73686 

72248 

70816 

!:!$ 

69390 
55440 

67969 
54076 

66554 
52718 

65H5 
51366 

63742 
50019 

48$ 

60952 
47341 

59566 
46011 

58185 
44687 

56810 
43368 

1.19 

42054 

40746 

39444 

36856 

35570 

34290 

33OI6 

3*747 

30483 

1.20 

9.9629225 

27973 

26725 

25484 

24248 

23017 

21792 

20573 

19358 

18150 

1.  21 

16946 

15748 

^369 

12188 

IIOII 

09841 

08675 

06361 

1.22 

05212 

04068 

02930 

01796 

00669 

99546 

98430 

973*8 

96212 

95*  ** 

1.23 

594015 

92925 

91840 

90760 

89685 

88616 

87553 

86494 

8544* 

84393 

1.24 

83350 

82313 

81280 

80253 

79232 

78215 

77204 

76198 

75*97 

74201 

1.25 

1.26 

9-95732" 
63592 

72226 
62658 

71246 
61730 

70271 
60806 

69301 

59888 

68337 
58975 

67377 
58067 

66423 

57*65 

6|474 
56267 

6453° 

55374 

1.27 

54487 

53604 

52727 

51855 

50988 

50126 

49268 

48416 

47570 

46728 

1.28 

45891 

45059 

44232 

434io 

42593 

41782 

40975 

40173 

39376 

38585 

1.29 

37798 

37016 

36239 

35467 

34700 

33938 

32439 

31682 

30940 

1.30 

9.9530203 

29470 

28743 

28021 

27303 

26590 

25883 

25180 

24482 

23789 

1.31 

23100 

22417 

21739 

21065 

20396 

19732 

19073 

18419 

17770 

17125 

1.32 

16485 
10353 

15850 
09766 

15220 
09184 

*4595 
08606 

13975 
08034 

'3359 
07466 

12748 
06903 

12142 
06344 

11540 
0579* 

10944 
05242 

i-34 

04698 

04158 

03624 

03094 

02568 

02048 

01532 

OIO2I 

00514 

00012 

1.35 

9-94995I5 

99023 

98535 

98052 

97573 

97100 

96630 

96166 

95706 

95251 

1.36 

94800 

94355 

939*3 

93477 

92617 

92194 

91776 

91362 

90953 

*-37 

9°549 

90149 

89754 

89363 

88977 

88595 

88218 

87846 

87478 

87II5 

1.38 

86756 

86402 

86052 

85707 

85366 

85030 

84698 

84371 

84049 

83731 

83417 

83108 

82803 

82503 

82208 

81916 

81630 

81348 

81070 

80797 

1.40 

1.41 

9.9480528 
78084 

80263 
77864 

80003 
77648 

79748 
77437 

79497 
7723° 

79250 
77027 

79008 
76829 

78770 
76636 

7?S3£ 
76446 

78308 
76261 

1.42 

76081 

75905 

75733 

75565 

75402 

75243 

75089 

74939 

74793 

74652 

1-43 
1.44 

74515 
73382 

74382 
73292 

74254 
73207 

74130 
73^5 

74010 
73°49 

73894 
72976 

73783 
72908 

73676 
72844 

73574 
72784 

73746 
72728 

*  Quoted  from  Carr's  "  Synopsis  of  Mathematics,"  and  is  there  quoted  from  Legendre's  "  Exercises  de  Calcul 
Integral,"  tome  ii. 

SMITHSONIAN  TABLES.  s 


TABLE  30  (continued}. 

GAMMA   FUNCTION. 


53 


n 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

1.45 

9.9472677 

72630 

72587 

72549 

725H 

72484 

72459 

72437 

72419 

72406 

1.46 

72397 

72393 

72392 

72396 

72404 

72416 

72432 

72452 

72477 

72506 

1.47 

72539 

72576 

72617 

72662 

72712 

72766 

72824 

72886 

72952 

73022 

1.48 

73097 

73*75 

73258 

73345 

73436 

73531 

73630 

73734 

73841 

73953 

1.49 

74068 

74188 

743  i  2 

74440 

74572 

74708 

74848 

74992 

75Hi 

75293 

1.50 

9-9475449 

75610 

75774 

75943 

76116 

76292 

76473 

76658 

76847 

77040 

i-5« 

1.52 

77237 
79426 

77438 
79667 

77642 
79912 

77851 
80161 

78064 
80414 

78281 
80671 

78502 
80932 

78727 
81196 

78956 
81465 

79189 
81738 

i-54 

82015 
84998 

82295 

82580 
85642 

82868 
85970 

83161 
86302 

83457 
86638 

83758 
86977 

84062 
87321 

84370 
87668 

84682 
88019 

1.55 

9.9488374 

88733 

89096 

89463 

89834 

90208 

90587 

90969 

9!355 

9I745 

1.56 

92139 

92537 

92938 

93344 

93753 

94166 

94583 

95004 

95429 

95.857 

1-57 

96289 

96725 

97165 

97609 

98056 

98508 

98963 

99422 

99885 

00351 

1.58 

500822 

01296 

01774 

02235 

02741 

03230 

03723 

04220 

04720 

05225 

i-59 

05733 

06245 

06760 

07280 

07803 

08330 

08860 

09395 

09933 

10475 

1.60 

9.9511020 

11569 

I2I22 

12679 

13240 

13804 

H372 

H943 

I55I9 

16098 

1.61 

16680 

17267 

17857 

18451 

19048 

19650 

20254 

20862 

2H75 

22O9I 

1.62 

22710 

23333 

23960 

24591 

25225 

25863 

26504 

27149 

27798 

28451 

1.63 
1.64 

29107 
35867 

29767 
36563 

30430 
37263 

31097 
37966 

31767 
38673 

32442 
39383 

33120 
40097 

33foi 
40815 

34486 
41536 

35175 
4226O 

1.65 

9.9542989 

43721 

44456 

45195 

45938 

46684 

47434 

48187 

48944 

49704 

1.66 

50468 

51236 

52007 

52782 

5356o 

54342 

55127 

55916 

56708 

57504 

1.67 

58303 

59106 

59913 

60723 

61536 

62353 

63174 

63998 

64826 

65656 

1.68 

66491 

67329 

68170 

69015 

69864 

70716 

7I57I 

7243° 

73293 

74159 

1.69 

75028 

75901 

76777 

77657 

78540 

79427 

80317 

81211 

82108 

83008 

1.70 

9.9583912 

84820 

85731 

86645 

87536 

88484 

89409 

90337 

21268 

92203 

1.71 

93  HI 

94083 

95028 

95977 

96929 

97884 

98843 

99805 

00771 

01740 

1.72 

602712 

03688 

04667 

06636 

07625 

08618 

09614 

I06I3 

Il6l6 

12622 

13632 

H645 

1  5661 

16681 

17704 

18730 

19760 

2O793 

21830 

1.74 

22869 

23912 

24959 

26009 

27062 

28118 

29178 

30241 

3*308 

32377 

1.75 

9-963345I 

34527 

35607 

36690 

37776 

38866 

39959 

41055 

42155 

43258 

1.76 

44364 

§473 

46586 

47702 

48821 

49944 

51070 

52200 

53331 

54467 

1.77 

556o6 

749 

57894 

59043 

60195 

61350 

62509 

63671 

64836 

66004 

1.78 

67176 

35i 

69529 

70710 

71895 

73082 

74274 

75468 

76665 

77866 

1.79 

79070 

80277 

81488 

82701 

83198 

85138 

86361 

87588 

88818 

90051 

1.80 

9.9691287 

92526 

93768 

950H 

96263 

97515 

98770 

00029 

01291 

0255; 

1.81 

703823 

05095 

06369 

07646 

08927 

IO2II 

11498 

12788 

14082 

1.82 

16678 

17981 

19287 

20596 

21908 

23224 

24542 

25864 

27189 

28517 

1  1-83 

29848 

31182 

32520 

33860 

35204 

36551 

37900 

39254 

40610 

41969 

1.84 

43331 

44697 

46065 

47437 

48812 

50190 

S'571 

52955 

54342 

55733 

1.85 

1.86 

9.9757126 
71230 

58522 
72657 

59922 
74087 

61325 

75521 

62730 
76957 

64140 
78397 

65551 
79839 

66966 
81285 

68384 
82734 

69805 
84186 

1.87 
1.88 
1.89 

85640 
800356 

87098 
01844 
16893 

88559 
03335 
I84H 

90023 
04830 
!9939 

91490 
06327 
21466 

92960 
07827 
22996 

94433 
09331 
2453° 

95910 
10837 
26066 

97389 
12346 
27606 

98871 

13859 
29148 

1.90 

9.9830693 

32242 

33793 

35348 

36905 

38465 

40028 

41595 

43l64 

44736 

1.91 
1.92 

46311 
62226 

47890 
63834 

4947  i 
65445 

67058 

^8675 

54232 
70294 

55825 
71917 

5742i 
73542 

59020 
75170 

60622 
76802 

1.93 

78436 

80073 

81713 

83356 

85002 

86651 

88302 

89957 

93275 

1.94 

9493s 

96605 

98274 

99946 

01621 

03299 

04980 

06663 

0835° 

10039 

1.95 

9.9911732 

13427 

15125 

16826 

18530 

20237 

21947 

23659 

25375 

27093 

1.96 

28815 

3°539 

32266 

33995 

35728 

37464 

39202 

40943 

42688 

1.97 

46185 

47937 

49693 

53213 

54977 

56744 

58513 

60286 

62062 

1.98 
1.99 

63840 
81779 

65621 
83588 

67405 
85401 

69192 
87216 

70982 
89034 

72774 
90854 

74570 
92678 

76368 
94504 

78169 
96333 

79972 
98165 

SMITHSONIAN  TABLES. 


54  TABLE  31 . 

ZONAL  HARMONICS.* 

The  values  of  the  first  seven  zonal  harmonics  are  here  given  for  every  degree  between  6  =  o°  and  0  =  90°. 


e 

Zl 

Z2 

z, 

z. 

Z5 

Z6 

z, 

0° 

I.OOOO 

I.OOOO 

I.OOOO 

I.OOOO 

I.OOOO 

I.OOOO 

I.OOOO 

1° 

0.9998 

0.9995 

0.9991 

0.9985 

0.9977 

0.9967 

0-9955 

2 

•9994 

.9982 

•9963 

•9939 

.9909 

.9872 

.9829 

3 

4 

.9986 
.9976 

•9959 

.9918 
.9854 

.9863 
•9758 

•9795 
.9638 

•9713 

•9495 

.9617 
•9329 

5 

.9962 

.9886 

•9773 

.9623 

•9437 

.9216 

.8961 

6° 

•9945 

.9836 

.9674 

•9459 

.9194 

.8881 

.8522 

7 

•9925 

•9777 

•9557 

.9267 

.8911 

.8476 

.7986 

8 

•9903 

.9709 

•9423 

.9048 

.8589 

•8053 

.7448 

9 

10 

.9877 
.9848 

•9633 
.9548 

•9273 
.9106 

.8803 
•8532 

.8232 
.7840 

•7571 
•7045 

.6831 
.6164 

11° 

.9816 

•9454 

.8923 

.8238 

•7417 

.6483 

.5461 

12 

.9781 

•9352 

.8724 

.7920 

.6966 

•5892 

•4732 

13 

•9744 

.9241 

.8511 

•7582 

.6489 

•5273 

•3940 

14 

•9703 

.9122 

.8283 

.7224 

•5990 

•4635 

.3219 

15 

.9659 

•8995 

.8042 

.6847 

•5471 

•3982 

•2454 

16° 

17 

.9613 
•9563 

.8860 
.8718 

.7787 

.6046 

•4937 
•4391 

•3322 
.2660 

.1699 
.0961 

18 

•9511 

.8568 

.7240 

.5624 

•3836 

.2002 

.0289 

19 

•9455 

.8410 

.6950 

.5192 

.3276 

•1347 

—•0443 

20 

•9397 

.8245 

.6649 

•475° 

•2715 

.0719 

—  .1072 

21° 

•9336 

.8074 

•6338 

.4300 

.2156 

.0107 

—.1662 

22 

.9272 

•7895 

.6019 

•3845 

.1602 

—  .0481 

—  .2201 

23 

.9205 

.7710 

.5692 

•3386 

•1057 

—.1038 

—.2681 

24 

•9135 

•7518 

•5357 

.2926 

•0525 

—  .1559 

—•3095 

25 

.9063 

.7321 

.5016 

.2465 

.0009 

—•2053 

—•3463 

26° 

.8988 

.7117 

.4670 

.2007 

—.0489 

—.2478 

—•3717 

27 

.8910 

.6908 

•4319 

•1553 

—.0964 

-.2869 

—.3921 

29 

.8829 
.8746 

.6694 
.6474 

.3964 
.3607 

.1105 
.0665 

—.1415 
-.1839 

—.3211 
—•35°3 

—.4052 
—.4114 

30 

.8660 

.6250 

.3248 

.0234 

—•2233 

—•3740 

—  .4101 

31° 

•8572 

.6021 

.2887 

—.0185 

—•2595 

—•3924 

—  .4022 

32 

.8480 

•5788 

.2527 

—.0591 

—•2923 

—.4052 

-•38/6 

33 

•8387 

•5551 

.2167 

—.0982 

—.3216 

—  .4126 

—.3670 

34 

.8290 

•5310 

.1809 

—•1357 

—•3473 

—.4148 

—•3409 

35 

.8192 

•5065 

•1454 

—.1714 

—.3691 

—•4115 

—.3096 

36° 

.8090 

.4818 

.1102 

—  .2052 

—•3871 

—.4031 

—2738 

37 

.7986 

•4567 

•0755 

—.2370 

—  .4011 

—3898 

—•2343 

38 

.7880 

•43H 

.0413 

—.2666 

—.4112 

—•3719 

—  .1918 

39 

.7771 

•4059 

.0077 

—.2940 

—.4174 

—•3497 

—.1469 

40 

.7660 

.3802 

—.0252 

—.3190 

—.4197 

—•3234 

—•1003 

41° 

•7547 

•3544 

—.0574 

—.3416 

—.4181 

—2938 

—  -°534 

42 

•7431 

.3284 

—.0887 

—.3616 

—.4128 

—  .2611 

—  .0065 

43 

•7314 

•3023 

—  .1191 

—  -3791 

—•4038 

—•225? 

•°395 

44 

•7193 

.2762 

-.I485 

—•3940 

—  -39J4 

—.1878 

.0846 

45 

.7071 

.2500 

—.1768 

—  .4062 

—•3757 

—.1485 

.1270- 

*  Calculated  by  Prof.  Perry  (Phil.  Mag.  Dec.  1891).     See  also  A.  Gray,  "Absolute  Measurements  in  Electricity 
and  Magnetism,"  vol.  ii.,  part  3.  — 

SMITHSONIAN  TABLES. 


TABLE  31  (continued). 
ZONAL   HARMONICS. 


55 


1 

zi 

Z2 

Zs 

z< 

n 

z. 

ZT 

46° 

0.6947 

0.2238 

—  .2040 

—.4158 

-.3568 

—.1079 

0.1666 

47 

.6820 

.1977 

—  .2300 

—4252 

—•3350 

—.0645 

.2054 

48 
49 

.6691 
.6561 

.1716 
.1456 

-.2547 
—  .2781 

—.4270 
—.4286 

—•3105 
—.2836 

-.0251 
.0161 

•2349 
.2627 

50 

.6428 

.1198 

—  .3002 

—4275 

—•2545 

•0563 

.2854 

51° 

.6293 

.0941 

—.3209 

—4239 

—•2235 

-0954 

•3°3r 

52 

53 

.6157 
.6018 

.0686 
•0433 

—.3401 
—3578 

-.4178 

—  .1910 
—•I57I 

.1326 
.1677 

•3153 
.3221 

54 
55 

.5878 
•5736 

.0182 
—  .0065 

-•$6 

-3852 

—.1223 
—.0868 

.2002 
-.2297 

•3234 
•3*91 

56° 

•5592 

—  .0310 

40l6 

—3698 

—.0510 

•2559 

•3095 

57 

•5446 

—•0551 

.4131 

—•3524 

—  .0150 

.2787 

.2949 

58 

•5299 

—.0788 

—4229 

—  -3331 

.0206 

.2976 

•2752 

59 

•5I5° 

—  .1021 

—4310 

—  -3«9 

.0557 

•3125 

.2511 

6o 

.5000 

—  .I25O 

—4375 

—.2891 

.0898 

.3232 

.2231 

61° 

.4848 

—.1474 

—4423 

—.2647 

.1229 

.3298 

.1916 

62 

.4695 

—  .1694 

—4455 

—.2390 

.1545 

•3321 

•1571 

63 

•4540 

—  .1908 

—.4471 

—.2121 

.1844 

•3302 

.1203 

64 

4384 

—.2117 

—.4470 

—.1841 

.2123 

,3240 

.0818 

65 

.4226 

—.2321 

—4452 

—•1552 

.2381 

•3138 

.0422 

66° 

.4067 

—.2518 

—.4419 

—  .1256 

.2615 

.2996 

.0021 

67 
68 

•3907 
•3746 

—  .2710 
—.2896 

—4370 
—4305 

—•0955 
—  .0650 

.2824 
•3005 

.2819 
.2605 

—  -°375 
—.0763 

69 

•3584 

—  -3°74 

—4225 

—•0344 

•3158 

.2361 

70 

.3420 

—•3245 

—.4130 

—.0038 

.3281 

.2089 

—•$5 

71° 

•3256 

—.3410 

—  .4021 

.0267 

•3373 

.1786 

—.1811 

72 
73 

.3090 
.2924 

-.3568 

-.3898 
—•376i 

^64 

•3434 
•3463 

.1472 
.1144 

—.2099 
—•2347 

74 

.2756 

—.'3860 

—  .3611 

•"53 

.3461 

•0795 

—•2559 

75 

.2588 

—•3995 

—•3449 

•1434 

•3427 

.0431 

—.2730 

76° 

.2419 

—  .4112 

—•3275 

•1705 

•3362 

.0076 

—.2848 

77 

.2250 

—.4241 

—.3090 

.1964 

.3267 

—  .0284 

—.2919 

78 

.2079 

—4352 

—.2894 

.2211 

•3143 

—.0644 

—•2943 

79 

.1908 

—4454 

—.2688 

•2443 

.2990 

—.0989 

—.2913 

80 

•1736 

—4548 

—•2474 

.2659 

.2810 

—.1321 

-•2835 

81° 

.1564 

—4633 

—.2251 

.2859 

.2606 

—.1635 

—.2709 

82 

.1392 

—.4709 

—  .2020 

.3040 

.2378 

—  .1926 

—•2536 

83 

.1219 

—4777 

—1783 

•3203 

.2129 

—.2193 

—•2321 

84 

.1045 

—  4836 

—  -'539 

.1861 

—.2431 

—  .2067 

85 

.0872 

—.4886 

—  .1291 

.3468 

•1577 

-.2638 

—.1779 

86° 

.0698 

—4927 

—.1038 

.3569 

.1278 

—.2811 

—  .1460 

87 

•0523 

—4959 

—.0781 

.3648 

.0969 

—.2947 

—.1117 

88 

•0349 

—.4982 

—  .0522 

•3704 

.0651 

—•3045 

—0735 

89 

.0175 

—4995 

—  .0262 

•3739 

.0327 

—•3105 

—.0381 

90 

.0000 

—  .5000 

—  .0000 

•3750 

.0000 

—•3125 

—  .0000 

SMITHSONIAN  TABLES. 


TABLE  32. 

MUTUAL  INDUCTANCE.* 
M 


M 


Table  of  values  of  log  — 17=  for  facilitating  the  calculation  of  the  mutual  inductance  M  of  two  coaxial  circles  of 

4*-V«*'  f(a_a/)2_l_£2>  J 

radii  a,  a',  at  distance  apart  b.    The  table  is  calculated  for  intervals  of  6/  in  the  value  of  cos-1  \  (g_a/\a  _L  ^2  j 
from  60°  to  90°. 


0' 

6' 

12' 

18' 

24' 

30' 

36' 

42' 

48' 

54' 

60° 

1.4994783 

5022651 

5050505 

5078345 

5106173 

5133989 

5161791 

5189582 

5217361 

5245128 

61 

5272883 

5300628 

5328361 

5356084 

5383796 

5411498 

5439*90 

5466872 

5494545 

5522209 

62 

5549864 

55775io 

5605147 

5632776 

5660398 

5688011 

5715618 

5743217 

5770809 

5798394 

63 

5825973 

5853546 

5881113 

5908675 

5936231 

5963782 

5991322 

6018871 

6046408 

6073942 

64 

6101472 

6128998 

6156522 

6184042 

6211560 

6239076 

6266589 

6294101 

6321612 

6349121 

65° 

1.6376629 

6404137 

6431645 

6459153 

6486660 

6514169 

6541678 

6569189 

6596701 

6624215 

66 

6651732 

6679250 

6706772 

6734296 

6761824 

6789356 

6816891 

6844431 

6871976 

6899526 

6? 

6927081 

6954642 

6982209 

7009782 

7037362 

7064949 

7092544 

7120146 

7H7756 

7175375 

68 

7203003 

7230640 

7258286 

7285942 

7313609 

7341287 

7368975 

7396675 

7424387 

7452111 

69 

7479848 

7507597 

753536i 

7563138 

7590929 

7618735 

7646556 

7674392 

7702245 

7730114 

70° 

1.7758000 

7785903 

7813823 

7841762 

7869720 

7897696 

7925692 

7953709 

7981745 

8009803 

7i 

8037882 

8065983 

8094107 

8122253 

8150423 

8178617 

8206836 

8235080 

8263349 

8291645 

72 

8319967 

8348316 

8376693 

8405099 

8433534 

8461998 

8490493 

8519018 

8547575 

8576164 

73 

8604785 

8633440 

8662129 

8690852 

8719611 

8748406 

8777237 

8806106 

8835013 

8863958 

74 

8892943 

8921969 

8951036 

8980144 

9009295 

9038489 

9067728 

9097012 

9126341 

9I557I7 

75° 

7.9185141 

9214613 

9244i35 

9273707 

9303330 

9333005 

9362733 

93925  l  5 

9422352 

9452246 

76 

9482196 

9512205 

9542272 

9572400 

9602590 

9632841 

9663157 

9693537 

9723983 

9754497 

77 

9785079 

98I5731 

9846454 

9877249 

9908118 

9939062 

9970082 

0001181 

0032359 

0063618 

78 

0.0094959 

0126385 

0157896 

0189494 

0221181 

0252959 

0284830 

0316794 

0348855 

0381014 

79 

04i3273 

0445633 

0478098 

0510668 

0543347 

0576136 

0609037 

0642054 

0675187 

0708441 

80° 

0.0741816 

07753J6 

0808944 

0842702 

0876592 

0910619 

0944784 

0979091 

1013542 

1048142 

81 

1082893 

1117799 

1152863 

1188089 

1223481 

1259043 

1294778 

1330691 

1366786 

1403067 

82 

J439539 

1476207 

1513075 

I550H9 

1587434 

1624935 

1662658 

1700609 

1738794 

1777219 

83 

1815890 

1854815 

1894001 

1933455 

1973184 

2013197 

2053502 

2094108 

2135026 

2176259 

84 

2217823 

2259728 

2301983 

2344600 

2387591 

2430970 

2474748 

2518940 

2563561 

2608626 

85° 

0.2654152 

2700156 

2746655 

2793670 

2841221 

2889329 

2938018 

2987312 

3037238 

3087823 

86 

3139097 

3191092 

3243843 

3297387 

3351762 

3407012 

3463184 

3520327 

3578495 

3637749 

87 

3698153 

3759777 

3822700 

3887006 

3952792 

4020162 

4089234 

4160138 

4233022 

4308053 

88 

4385420 

4465341 

4548064 

4633880 

4723127 

4816206 

4913595 

5015870 

5123738 

5238079 

89 

5360007 

5490969 

5632886 

5788406 

5961320 

6i5737o 

6385907 

6663883 

7027765 

7586941 

*  Quoted  from  Gray's 
SMITHSONIAN  TABLES. 


'Absolute  Measurements  in  Electricity  and  Magnetism,"  vol.  ii.,  p.  852. 


TABLE  33. 
ELLIPTIC   INTEGRALS. 


57 


Values  ol  I  3(1- sin2*  sin2  $)**<*£. 

Jo 

This  table  gives  the  values  of  the  integrals  between  o  and  ir / 2  of  the  function  (i — sin2 0 sin2 $)      d$  for  different  val- 
ues of  the  modulus  corresponding  to  each  degree  of  6  between  o  and  90. 


9 

rs  d* 

Cv 

Jo 

1 

Cl   # 

f  *(i  sin^sin   »</ 

Jo 

^/O   (i—  sin20sin2<J>)* 

J0  (,-»»*«**)» 

Number. 

Log. 

Number. 

Log. 

Number. 

Log. 

Number. 

Log. 

0° 

1.5708 

0.196120 

1.5708 

0.196120 

45° 

1.8541 

0.268127 

I-3506 

0.130541 

I 

5709 

I96I53 

5707 

196087 

6 

8691 

271644 

3418 

127690 

2 

5713 

196252 

5703 

195988 

7 

8848 

275267 

3329 

124788 

3 

5719 

196418 

195822 

8 

9OII 

279001 

3238 

121836 

4 

5727 

196649 

5^9 

I9559I 

9 

9180 

282848 

3*47 

118836 

5° 

1.  5738 

0.196947 

1.5678 

0.195293 

50° 

L9356 

0.2868II 

1-3055 

0.115790 

6 

5751 

197312 

5665 

194930 

i 

9539 

290895 

2963 

112698 

I 

5767 
5785 

197743 
198241 

5649 
5632 

194500 
194004 

2 

3 

9729 
9927 

295IOI 
299435 

2870 
2776 

109563 
106386 

9 

5805 

198806 

5611 

193442 

4 

2.0133 

303501 

2681 

103169 

10° 

1.5828 

0.199438 

L5589 

0.192815 

55° 

2-0347 

0.308504 

1.2587 

0.099915 

i 

5854 

200137 

5564 

192121 

6 

0571 

313247 

2492 

096626 

2 

5882 

200904 

5537 

1913(32 

7 

0804 

318138 

2397 

093303 

3 
4 

5913 
5946 

201740 
202643 

5507 
5476 

190537 
189646 

9 

1047 
1300 

323182 
328384 

2301 
2206 

089950 
086569 

15° 

I.598I 

0.203615 

1.5442 

0.188690 

60° 

2.1565 

0-333753 

I.2III 

0.083164 

6 

6O2O 

204657 

5405 

187668 

i 

1842 

339295 

2OI5 

079738 

7 

6061 

205768 

5367 

I8658I 

2 

2132 

345020 

1920 

076293 

8 

6105 

206948 

5326 

185428 

3 

2435 

350936 

1826 

072834 

9 

6151 

208200  . 

5283 

184210 

4 

2754 

357053 

1732 

069364 

20° 

1.6200 

0.209522 

1.5238 

0.182928 

65° 

2.3088 

0.363384 

1.1638 

0.065889 

i 

6252 

210916 

181580 

6 

3439 

369940 

*545 

062412 

2 

6307 

212382 

5141 

180168 

7 

3809 

376736 

1453 

058937 

3 

6365 

213921 

5090 

178691 

8 

4198 

383787 

1362 

055472 

4 

6426 

215533 

5037 

I77I50 

9 

4610 

39III2 

1272 

052020 

25° 

1.6490 

0.217219 

1.4981 

0.175545 

70° 

2.5046 

0.398730 

1.1184 

0.048589 

6 

6557 

218981 

4924 

173876 

i 

55°7 

406665 

1096 

045l83 

7 

6627 

2208l8 

4864 

172144 

2 

5998 

4M943 

ion 

041812 

8 

6701 

222732 

4803 

170348 

3 

6521 

423596 

0927 

038481 

9 

6777 

224723 

4740 

168489 

4 

7081 

432660 

0844 

035200 

30° 

i 

1.6858 
6941 

0.226793 
228943 

1.4673 
4608 

0.166567 
164583 

75° 

6 

2.7681 
8327 

0.442176 
452196 

1.0764 
0686 

0.031976 
028819 

2 

7028 

23H73 

4539 

162537 

7 

9026 

462782 

0611 

025740 

3 

7119 

233485 

4469 

160429 

8 

9786 

474008 

0538 

022749 

4 

7214 

235880 

4397 

158261 

9 

3-0617 

485967 

0468 

019858 

35° 

I.73I2 

0.238359 

1.4323 

0.156031 

80° 

3.1534 

0.498777 

1.0401 

0.017081 

6 

7415 

240923 

4248 

153742 

i 

2553 

5I259I 

0338 

014432 

7 

7522 

243575 

4171 

I5I393 

2 

3699 

527613 

0278 

011927 

8 

7633 

246315 

4092 

148985 

3 

5004 

544120 

0223 

009584 

9 

7748 

249146 

4013 

146519 

4 

6519 

562514 

0172 

007422 

40° 

i 

1.7868 
7992 

0.252068 

255085 

I-393I 

0.143995 
141414 

85° 

6 

3-8317 
4.0528 

0.583396 
607751 

1.0127 
0086 

0.005465 
003740 

2 

8122 

258197 

3765 

138778 

7 

3387 

637355 

0053 

002278 

3 

8256 

261406 

3680 

136086 

8 

7427 

676027 

0026 

OOII2I 

4 

8396 

264716 

3594 

1  33  340 

9 

5-4349 

735192 

0008 

OOO326 

45° 

1.8541 

0.268127 

1.3506 

0.130541 

90° 

CO 

00 

1.  0000 

SMITHSONIAN  TABLES. 


$8  TABLE  34. 

MOMENTS  OF  INERTIA,  RADII  OF  GYRATION,  AND  WEIGHTS. 

In  each  case  the  axis  is  supposed  to  traverse  the  centre  of  gravity  of  the  body.    The  axis  is 
one  of  symmetry.     The  mass  of  a  unit  of  volume  is  w. 


Body. 

Axis. 

1 

Weight. 

Moment  of  Inertia  Io. 

Square  of  Ra- 
dius of  Gyra- 
tion p2. 

r* 

Rir"?>r& 

2 

Sphere  of  radius  r 

Diameter 

47Tw// 

£r 

3 

15 

5 

Spheroid  of  revolution,  po- 
lar axis  20,  equatorial  di- 

Polar axis 

4irwar2 

Sinvar* 

2^2 

f 

ameter  2r 

3 

15 

5 

Ellipsoid,  axes  20,  2b,  20 

Axis  20, 

qirwabc 
3 

4.irwabc(bz+c*  ) 

^2+^2 

IS 

5 

Spherical  shell,  external  ra- 
dius r,  internal  r' 

Diameter 

47rw(r3  —  r's) 

Sirzvir6  —  r'5) 

2(r5  —  ^/5) 

3 

15 

S(r8—r/s) 

Ditto,  insensibly  thin,  ra- 
dius r,  thickness  dr 

Diameter 

<»*&. 

&irwr*dr 

2r* 

3 

3 

Circular  cylinder,  length  2a, 
radius  r 

Longitudinal 
axis  20, 

«*H 

irwar* 

2 

Elliptic  cylinder,  length  20, 
transverse  axes  2b,  2c 

Longitudinal 
.  axis  20, 

2-trwabc 

•Kwabc(P-\-c*) 

jy-^j 

2 

4 

Hollow    circular    cylinder, 
length    2a,  external    ra- 
dius r,  internal  r1 

Longitudinal 
axis  20, 

~-w 

~+*-^ 

2 

Ditto,  insensibly  thin,  thick- 
ness dr 

Longitudinal 
axis  20 

qmuardr 

Vrw^dr 

r* 

Circular  cylinder,  length  2a, 
radius  r 

Transverse 
diameter 

2-tnuar2 

invar1  (  yz-\-  40?) 

r*     a* 

6 

4+3 

Elliptic  cylinder,  length  2a, 

Transverse 

irwabc(y'1-{-4[a'2') 

c<i  i  ^ 

transverse  axes  2a,  2b 

axis  2b 

6 

43 

Hollow   circular    cylinder, 

Transverse 

mva  1  ^-r'*)           ) 

r2+r'2      «2 

dius  r>  internal  r1 

diameter 

r  ) 

6    }    +4^2(^2-^)  ; 

4      "*"  3 

Ditto,  insensibly  thin,  thick- 
ness dr 

Transverse 
diameter 

^irwardr 

3 

¥+3 

Rectangular  prism,  dimen- 
sions 2a,  2b,  2c 

Axis  20, 

Swabc 

8wabc(l>2+^) 

3 

3 

Rhombic  prism,  length  20, 
diagonals  2b,  2c 

Axis  2a 

qwabc 

zwabctft+c1) 

^2-fr2 

3 

6 

Ditto 

Diagonal  2b 

tpvabc 

2wabc(c  2+2a2) 

^ai 

3 

(Taken  from  Rankine.) 


SMITHSONIAN  TABLES. 


TABLES  35-36. 
BRITISH  GAUGE  NUMBERS  AND  SIZES  OF  WIRES. 

For  Brown  &  Sharp  American  Gauge  and  Electrical  Constants  see  Tables  40  and  41. 
TABLE  35.  —British  Standard  Wire  Gauge.  TABLE  36.  —  Birmingham  Wire  Gauge. 


59 


aS 

<M 

Diameter  in  I 
Inches. 

Section  in 
Sq.  Inches. 

Diameter 
in  Centi- 
metres. 

Section  in 
Sq.  Cms. 

7-0 

0.500 

0.1963 

1.2700 

1.267 

6-0 

.464 

.1691 

.1786 

.091 

5-o 

0.432 

0.1466 

1.0973 

0.9456 

4-0 

.400 

•1257 

.0160 

.8107 

3-o 

•372 

.I087 

0.9449 

.7012 

2-0 

.348 

.0951 

.8839 

.6136 

0 

.324 

.0825 

.8230 

•53*9 

1 

0.300 

0.07069 

0.7620 

0.4560 

2 

.276 

•05983 

.7010 

.3858 

3 

.252 

.04988 

.6401 

.3218 

4 

.232 

.04227 

•5893 

.2727 

5 

.212 

•03530 

•5385 

.2277 

6 

0.192 

0.02895 

0.4877 

0.18679 

7 

.176 

•02433 

.4470 

.15696 

8 

.100 

.O2OIO 

.4064 

•12973 

9 

.144 

.01629 

.3658 

.10507 

10 

.128 

.01287 

•3251 

.08302 

11 

0.116 

0.010568 

0.2946 

0.06818 

12 

.104 

.00849^ 

.2642 

.05480 

13 

.092 

.006648 

•2337 

.04289 

14 

.080 

.005027 

.2032 

.03243 

IS 

.072 

.00407  1 

.1829 

.02627 

16 

0.064 

0.003217 

0.16256 

0.020755 

17 

.056 

.002463 

.14224 

.015890 

18 

.048 

.OOlSlO 

.12192 

•011675 

*9 

.040 

.001257 

.I0l6o 

.008107 

20 

.036 

.OOIOlS 

.09144 

.006567 

21 

0.032 

0.0008042 

0.08128 

0.005189 

22 

.028 

.00061  58 

.07112 

.003973 

23 

.024 

.0004524 

.06096 

.002922 

24 

.022 

.0003801 

.05588 

.002452 

25 

.020 

.0003142 

.05080 

.002027 

26 

0.0180 

0.0002545 

0.04572 

0.0016417 

27 

.0164 

.0002112 

.04166 

.0013628 

28 

.0148 

.OOOI728 

•03759 

.0011099 

29 

.0136 

.0001453 

•03454 

.0009363 

30 

.0124 

.0001208 

.03150 

.0007791 

31 

0.0116 

0.00010568 

0.02946 

0.0006818 

32 

.0108 

.OOOO9l6l 

.02743 

.0005910 

33 

.0100 

.00007854 

.02540 

.0005067 

34 

.0092 

.00006648 

.02337 

.0004289 

35 

.0084 

.00005542 

.02134 

.0003575 

36 

0.0076 

0.00004536 

0.01930 

0.0002927 

* 

.0068 
.0060 

.00003632 
.OOOO2827 

.01727 
.01524 

.0002343 
.0001824 

39 
40 

.0052 
.0048 

.00002124 
.OOOOlSlO 

.01321 
.01219 

.0001370 
.0001167 

41 

0.0044 

O.OOOOI52I 

O.OIIlS 

0.0000982 

42 

.0040 

.OOOOI257 

.OIOl6 

.0000811 

43 

.0036 

.OOOOIOlS 

.00914 

.0000656 

44 

.0032 

.OOOOO8O4 

.00813 

.0000519 

45 

.0028 

.0000o6l6 

.00711 

.0000397 

46 

0.0024 

0.00000452 

0.00610 

0.0000292 

4£ 

.0020 

.OOOOO3I4 

.00508 

.0000203 

48 

.0016 

.OOOOO2OI 

.00406 

.0000129 

49 

.0012 

.OOOOOII3 

.00305 

.0000073 

50 

.0010 

.OOOOOO79 

.00254 

.0000051 

4>   tU 

P 
*& 

Diameter  in  I 
Inches. 

Sections  in 
Sq.  Inches. 

Diameter 
in  Centi- 
metres. 

Section  in 
Sq.  Cms. 

0000 

0-454 

0.16188 

I-I532 

1.0444 

000 

425 

.14186 

•0795 

.9152 

oo 

.380 

.11341 

0.9652 

•7317 

0 

•340 

.09079 

.8636 

•5858 

1 

0.300 

0.07069 

0.7620 

0.4560 

2 

.284 

.06335 

.7214 

.4087 

3 

•259 

.05269 

.6579 

•3399 

4 

.238 

.04449 

.6045 

.2870 

5 

.220 

.03801 

•5588 

.2452 

6 

0.203 

0.03237 

0.5156 

0.20881 

I 

.180 
.165 

•0254<> 
.02138 

•4572 
.4191 

.16417 
•J3795 

9 

.148 

.01720 

•3759 

.11099 

10 

•134 

.01410 

•3404 

.09098 

11 

0.120 

0.011310 

0.3048 

0.07297 

12 

.I09 

.009371 

.2769 

.06160 

13 

•095 

.007088 

.2413 

•04573 

14 

.083 

.005411 

.2108 

.03491 

IS 

.072 

.004072 

.1829 

.02627 

16 

0.065 

0.0033183 

0.16510 

0.021409 

17 

.058 

.0026421 

•14732 

.017046 

18 
J9 

.049 
.042 

.0018857 
.0013854 

.12446 
.10668 

.012166 
.008938 

20 

•035 

.0009621 

.08890 

.006207 

21 

0.032 

0.0008042 

0.08128 

0.005189 

22 

.028 

.0006158 

.07112 

•003973 

23 

.025 

.0004909 

•06350 

.003167 

24 

.022 

.0003801 

.05588 

.002452 

25 

.020 

.0003142 

.05080 

.002027 

26 

0.018 

0.0002545 

0.04572 

0.0016417 

27 

.Ol6 

.0002011 

.04064 

.0012972 

28 

.014 

.0001539 

•03556 

.0009932 

29 

.013 

.0001327 

.03302 

.0008563 

30 

.012 

.OOOIlSl 

.03048 

.0007297 

31 

32 

0.010 
.009 

0.00007854 
.00006362 

0.02540 
.02286 

0.0005067 
.0004104 

33 
34 
35 

.008 
.007 
.005 

.00005027 
.00003848 
.00001963 

.02032 
.01778 
.01270 

.0003243 
.0002483 
.0001267 

36 

0.004 

0.00001257 

0.01016 

0.0000811 

SMITHSONIAN  TABLES. 


6o 


TABLE  37. 
BRITISH   UNITS. 

Cross  sections  and  weights  of  wires. 


This  table  gives  the  cross  section  and  weights  in  British  units  of  copper,  iron,  and  brass  wires  of  the  diameters 
iven  in  the  first  column.  For  one  tenth  the  diameter  divide  section  and  weights  by  100.  For  ten  times  the 
iameter  multiply  by  100,  and  so  on. 


gi 
di 


If 

5 

Area  of 
cross 
section 
in 
Sq.  Mils. 

Copper  —  Density  8.90. 

Iron  —  Density  7.80. 

Brass—  Density  8.56. 

Pounds 
per  Foot. 

Log. 

Feet  per 
Pound. 

Pounds 
per  Foot. 

Log. 

Feet  per 
Pound. 

Pounds 
per  Foot. 

Log. 

Feet  per 
Pound. 

10 

78.54 

.000303 

4.48150 

33°0- 

.0002656 

4.42420 

3765. 

.000291  5 

4.46458 

343  1- 

ii 

95-03 

0367 

•56429 

2727. 

03214 

•50697 

3II2. 

03527 

54735 

2836. 

12 

113.10 

0436 

.63986 

2291. 

0382; 

-58257 

2615. 

04197 

62295 

2383- 

13 

132.73 

0512 

•70939 

1953. 

04488 

.65208 

2228. 

04926 

69246 

2030. 

14 

153-94 

0594 

•77376 

1683. 

05206 

.71646 

1921. 

05713 

75684 

1750- 

15 

16 

176.71 
2OI.O6 

.000682 
0776 

4.83368 
.88974 

1467. 
1289. 

.0005976 
06799 

4.77637 
.83244 

1674. 
1471. 

.0006558 
07461 

4.81675 

.87282 

1525- 
1340. 

17 

226.98 

0876 

.94240 

1142. 

07675 

.88510 

I3°3- 

08423 

.92548 

1187. 

18 

25447 

0982 

•99205 

1018. 

08605 

•93475 

1162. 

09443 

•975*3 

1059. 

19 

283.53 

1094 

3-03902 

914. 

09588 

.98171 

1043. 

.0010522 

3.02209 

950- 

20 

314.16 

.OOI2I2 

3-08357 

825.1 

.001062 

3.02626 

941.4 

.OOIl66 

3.06664 

857-7 

21 

22 

346.36 
380.13 

J336 
1467 

.12594 
.16634 

748.3 
681.8 

II7I 
1286 

.06864 
.10904 

777-8 

1285 
I4II 

.10902 
.14942 

778.0 
708.9 

23 

415.48 

1603 

.20496 

623.8 

1405 

.14766 

711.7 

1542 

.18804 

648.6 

24 

452-39 

1746 

.24192 

572.9 

1S3° 

.18463 

653-7 

1679 

.22500 

595-7 

25 

490.87 

.001894 

3.27738 

528.0 

.001660 

3.22008 

602.4 

.OOl822 

3.26046 

549-o 

26 

530-93 

2046 

.31146 

488.1 

1795 

•25415 

557-o 

1970 

•29453 

507-5 

27 

572.56 

2209 

•34423 

452.6 

1936 

.28693 

5*6-5 

2125 

•3273* 

470.6 

28 

6I5-75 

2376 

•37583 

420.9 

2082 

•31852 

480.3 

2285 

•35890 

437-6 

29 

660.52 

2549 

.40630 

3924 

2234 

.34900 

447-7 

245  ! 

•38938 

408.0 

30 

706.86 

.002727 

3-43575 

366.7 

.002390 

3-37845 

418.4 

.002623 

3.41882 

381.2 

32 

754-77 
804.25 

2912 
3I03 

.46424 
.49181 

343-4 
322.2 

2552 
2720 

.40693 
•4345° 

391.8 

2801 
2985 

-44731 
.47488 

357-0 
335-1 

33 
34 

855-30 
907.92 

35°3 

•51854 
•54446 

303-0 
285.4 

2892 
3070 

.46123 
.48716 

345-8 

3369 

.50161 

•52754 

3I5-1 
296.8 

35 

962.11 

.003712 

3-56964 

269.4 

•003253 

3-5I233 

307-4 

.003570 

3-5527I 

280.1 

36 

1017.88 

3927 

.59412 

254.6 

3442 

•53691 

290.5 

3777 

•57719 

264.7 

37 

1075.21 

4149 

.61791 

241.0 

3636 

.56061 

275-o 

3990 

.60098 

250.6 

38 
39 

1134.11 
1194.59 

4376 
4609 

.64108 
.66364 

228.5 
216.9 

3844 
4040 

.58476 
•60633 

260.2 
247.6 

4218 
4433 

.62514 
.64671 

237-1 
225.6 

40 

1256.64 

.004849 

3-68563 

206.2 

.004249 

3-62833 

235-3 

.004664 

3.66871 

214.4 

41 

1320.25 

5°94 

.70708 

196.3 

4465 

•64977 

224.0 

4900 

.69015 

204.1 

42 

I385-44 

5346 

.72801 

187.1 

4685 

.67070 

213-5 

5141 

.71108 

1^4.5 

43 

1452.20 

5603 

.74845 

178.5 

4911 

.69114 

203.6 

5389 

.73152 

185.6 

44 

1520.53 

5867 

.76842 

170.4 

5J42 

.71111 

'94-5 

5643 

•75*49 

177.2 

45 

46 

159043 
1661.90 

.006137 
6412 

3-78793 
•80703 

162.9 
J55-9 

.005378 
5620 

3-73063 

.74972 

185.9 
177.9 

.005902 

3.77101 
.79010 

169.4 
162.1 

47 

1734-94 

6694 

.82569 

149.4 

5867 

.76840 

170.5 

6438 

.80878 

J55-3 

48 

1809.56 

6982 

•84399 

143.2 

6119 

.78669 

163.4 

6715 

.82706 

148.9 

49 

1885.74 

7276 

.86189 

137-4 

6377 

.80459 

156.8 

6o9S 

•84497 

142.9 

50 

51 

1963.50 
2042.82 

•007576 
7882 

3-87945 
.89664 

132.0 
126.9 

.006640 
6908 

3.82214 
•83934 

150.6 

144.8 

.007287 
7581 

3.86252 
.87972 

137-2 

52 
53 
54 

2123.72 
2206.18 
2290.22 

8194 
8512 
8837 

•91352 
•93005 
.94630 

I22.O 

"7-5 

113.2 

7181 
746o 
7744 

.85621 

•87275 
.88899 

139.2 
134.0 
129.1 

8187 
8499 

.89659 
•92937 

126.9 

I22.I 
1177 

55 

2375.83 

.009167 

3.96223 

109.1 

.008034 

3-90493 

124.5 

.008817 

3-94531 

"3-4 

SMITHSONIAN  TABLES. 


TABLE  37  (continued). 

BRITISH  UNITS. 

Cross  sections  and  weights  of  wires. 


61 


a 

"4 

2  ^ 
Q 

Area  of 
cross 
section 

Sq.  Mils. 

Copper  —  Density  8.90. 

Iron  —  Density  7.80. 

Brass  —  Density  8.56. 

Pounds 
per  Foot. 

Log. 

Feet  per 
Pound. 

Pounds 
per  Foot. 

Log. 

Feet  per 
Pound. 

Pounds 
per  Foot. 

Log. 

Feet  per 
Pound. 

55 

56 

P 

2375-83 
2463.01 
255I-76 
2642.08 

.009167 
09504 
09846 
10195 

3.96223 
.97789 

.99325 
2.00837 

109.1 
105.2 

101.6 
98.1 

.008034 
08329 
08629 
08934 

3-90493 
.92058 

-93595 
.95106 

124.5 
1  20.  1 

"5-9 
111.9 

.008817 
09140 
09470 
09805 

3-94531 
.96096 

.97633 
.99144 

II3-4 
109.4 
105.6 
IO2.O 

59 

2733-97 

10549 

.02320 

94.8 

09245 

.96591 

108.2 

10146 

2.00629 

98.6 

60 

2827.43 

.01091 

2.03782 

91.66 

.00956 

3.98050 

104.59 

.01049 

2.02088 

95-30 

61 

2922.47 

1128 

.05216 

88.68 

0988 

.99486 

101.19 

1085 

•03524 

92.21 

62 

3019.07 

1165 

.06628 

85.84 

IO2I 

2.00898 

97-95 

II2O 

.04936 

89.25 

63 

3I][7-25 

1203 

.08019 

83.14 

1054 

.02288 

94-87 

"57 

.06326 

86.45 

64 

3216.99 

1241 

.09386 

80.56 

1088 

•03656 

91.83 

1194 

.07694 

8377 

65 

3318.31 

.01280 

2.10732 

78.11 

.01122 

2.05003 

89.12 

.01231 

2.09041 

8l.2I 

66 

3421.19 
3525-65 

1320 
1360 

.12061 
•13367 

75-76 
73-5i 

1157 
1192 

.06329 
•07635 

86.44 
83.88 

1270 
1308 

.10367 
.11673 

78.76 
76.43 

68 

3631.68 

I4OI 

.14655 

71-36 

1228 

.08922 

81.42 

1348 

.12960 

74.20 

69 

3739-28 

1443 

.15924 

69.30 

1264 

.10190 

79.09 

1388 

.14228 

72.06 

70 

384845 

.01485 

2.17174 

67-34 

.01302 

2.11451 

76.82 

.01429 

2.15489 

70.00 

7i 

39  59-  i  9 

1528 

.18404 

65.46 

1339 

74.69 

1469 

.16710 

68.06 

I  72 

4071.50 

1571 

.19618 

63-65 

1377 

.13887 

72.63 

'5" 

•17925 

66.19 

73 

4185.39 

1615 

.20817 

61.92 

HI5 

.15085 

70.66 

J553 

.19123 

64.38 

74 

4300.84 

1660 

.22OOO 

60.26 

1454 

.16267 

68.76 

J596 

.20304 

62.66 

75 

4417.86 

.01705 

2.23165 

58.66 

.01494 

2.17432 

66.95 

.01639 

2.21460 

61.01 

76 

4536-46 

I751 

•243  i  7 

57-13 

J534 

•18583 

65.19 

1684 

.22621 

59-40 

77 
78 

4656.63 
4778.36 

1797 
1844 

•25453 
.26574 

55-65 
54-23 

IIII 

.19718 
.20839 

63.50 
61.89 

1728 
1773 

•23756 
.24877 

57-87 
56.39 

79 

4901.67 

1892 

.27681 

52.87 

1658 

.21946 

60.33 

1819 

•25974 

54-99 

80 

5026.55 

.01939 

2.28769 

51-56 

.01700 

2.23038 

58.83 

.01865 

2.27076 

53-6i 

81 

5  1  53-0° 

i9& 

.29848 

50-29 

T743 

.24117 

57-39 

1912 

•28155 

52.29 

82 

5281.02 

2038 

.30914 

49.07 

1786 

•25183 

56.00 

1960 

.29221 

5*-93 

83 

5410.61 

2088 

.31966 

47.90 

1830 

.26236 

54.66 

2008 

.30274 

49-80 

84 

5541-77 

2138 

.33006 

46.77 

1874 

.27276 

53-36 

2057 

.3I3M 

48.63 

85 

5674-50 

.02189 

2.34034 

45-67 

.01919 

2.28304 

52.11 

.02106 

2.32342 

47-49 

86 

5808.80 

2241 

•35050 

44.62 

1964 

.29320 

50.91 

2156 

.33358 

46-39 

87 

5944-68 

2294 

•36054 

43.60 

2OIO 

.30324 

49-75 

2206 

.34362 

45-33 

88 

6082.12 

2347 

.37047 

42.61 

2057 

•a'a1? 

48.62 

2257 

•35355 

44-3° 

89 

6221.14 

2400 

.38028 

41.66 

2IO4 

•32298 

47-54 

2309 

.36336 

43-31 

90 

6361.73 

•02455 

2.38999 

40.74 

.02151 

2.33269 

46.49 

.02360 

2.37297 

42.37 

91 

6503.88 

2509 

•39958 

39.85 

2199 

.34228 

45-47 

2414 

.38266 

41.43 

92 

6647.61 

2565 

.40908 

38-99 

2248 

•35178 

44-49 

2467 

.39216 

40-54 

93 
94 

6792.91 
6939-78 

2621 
2678 

.41847 
42775 

38-15 
37-35 

2297 
2347 

.36116 
.37046 

43-54 
42.61 

2521 
2575 

.40154 
.41084 

39-67 
38-83 

95 

7088.22 

•02735 

2.43694 

36.56 

.02397 

2.37965 

41.72 

.02630 

2.42003 

38.02 

96 

7238.23 

2793 

.44604 

35-8i 

2448 

.38874 

40.86 

2686 

.42912 

37-23 

9l 

7389.81 

2851 

.45504 

35-07 

2499 

.39775 

40.02 

2742 

.43812 

36.46 

98 

7542.96 

2910 

46395 

34-36 

2551 

.40665 

39.20 

2799 

.44703 

35-72 

99 

7697.69 

2970 

.47277 

33.67 

2003 

•4!547 

38.42 

2857 

45585 

35-oi 

100 

7853.98 

.03030 

2.48150 

33-00 

.02656 

2.42420 

37.65 

.02915 

2.46458 

34.31 

SMITHSONIAN  TABLES. 


62  TABLE  38. 

METRIC  UNITS. 

Cross  sections  and  weights  of  wires. 

This  table  gives  the  cross  section  and  the  weight  in  metric  units  of  copper,  iron,  and  brass  wires  of  the  diameters 
given  in  the  first  column.  For  one  tenth  the  diameter  divide  sections  and  weights  by  100.  For  ten  times  the 
diameter  multiply  by  100,  and  so  on. 


Diam.  in  thou- 
sandths of  a  cm.  1 

Area  of  cross 
section  (jc0^0)s 

Copper  —  Density  8.90. 

Iron  —  Density  7.80. 

Brass  —  Density  8.56. 

J*j 

Log. 

5  J 

1*3 

L 

Is! 

Log. 

Metres 
per 
Gramme. 

Ill 

&** 

Log. 

Metres 
per 
Gramme. 

10 

78.54 

0.06990 

2.84448 

14.306 

0.06126 

2.78718 

16.324 

0.06723 

2.82756 

14.874 

ii 

95-03 

.08458 

,-92725 

11.823 

.07412 

.86996 

13.492 

•08135 

.91034 

12.293 

12 
13 

113.10 
132.73 

.10065 
.11813 

1.00285 
.07236 

9-935 
8.465 

.08822 
•!0353 

_-94556 
1.01506 

n-335 
9-659 

.09681 
.11362 

_.98594 
1-05544 

10.330 
8.801 

14 

153.94 

.13701 

.13674 

7.299 

.12008 

•07945 

8.328 

'13*71 

.11983 

7.589 

15 

176.71 

0-I573 

1.19665 

6.358 

0.1378 

7-I3936 

7-255 

0-1513 

1.17974 

6.611 

16 

2OI.O6 

.1789 

.25272 

5.588 

.1568 

•19542 

6.376 

.1721 

•2358o 

5.810 

17 

226.98 

.2020 

•30538 

4-951 

.1770 

.24808 

5.648 

•1943 

.28846 

5-H7 

18 
19 

254-47 
283.53 

.2265 
•2523 

•35503 
.40199 

4415 
3-963 

.1985 

.2212 

•29773 
•34469 

5-038 
4-522 

.2178 
•2427 

•338ii 
•38507 

4-591 
4.120 

20 

314.16 

0.2796 

1.44654 

3-577 

0.2450 

1.38925 

4.081 

0.2689 

1.42963 

3-7I9 

21 

346.36 

.3083 

.48892 

.244 

.27O2 

.43162 

3.701 

.2965 

.47200 

•373 

22 

380.13 

•52932 

2.956 

.2965 

.47203 

•373 

•3254 

.51241 

•073 

23 

415.48 

.3698 

•56794 

.704 

•3241 

.51064 

.086 

•3557 

•55103 

2.812 

24 

452.39 

.4026 

.60490 

.484 

•3529 

•5476i 

2.834 

•3872 

•58799 

,582 

25 

490.87 

0.4369 

1.64036 

2.289 

0.3829 

1.58306 

2.612 

0.4202 

1.62344 

2.380 

26 

530.93 

4725 

•67443 

.116 

.4141 

.61713 

415 

4545 

•65751 

.200 

27 

572.56 

.5096 

.70721 

1.962 

.4466 

.64992 

•239 

.4901 

.69030 

.040 

28 

6I575 

.5480 

.73880 

.825 

.4803 

.68150 

.082 

•5271 

.72188 

1.897 

29 

660.52 

•5879 

.76928 

.701 

•5152 

.71198 

1.941 

•5654 

•75236 

.769 

30 

706.86 

0.6291 

1.79872 

1.590 

o-55J4 

^•74143 

1.814 

0.6051 

1.78181 

1-653 

3i 

754-77 

.6717 

.82721 

.489 

.76991 

.699 

.6461 

.81029 

.548 

32 

804.25 

.7158 

.85478 

•397 

•6273 

•79749 

•594 

.6884 

•83787 

453 

33 

855-30 

.7612 

.88151 

•3*4 

.6671 

.82421 

•499 

.7321 

.86459 

34 

907.92 

.8o8l 

.90744 

.238 

.7082 

.85014 

.412 

.7772 

.89052 

.'287 

35 

962.11 

0.856 

7.93261 

1.168 

0.7504 

7-87531 

1-333 

0.8236 

1.91570 

1.214 

36 

1017.88 

.906 

•95709 

.104 

•7939 

•89979 

.260 

•8713 

.94017 

.148 

37 

1075.21 

•957 

.98088 

•°45 

.8387 

•92359 

.192 

.9204 

.96397 

.087 

38 

1134.11 

I.OI2 

0.00504 

0.988 

.8866 

•94775 

.128 

•9730 

.98813 

.028 

39 

1194.59 

•063 

.02661 

.941 

.9318 

.96931 

•073 

1.0230 

0.00969 

0.978 

40 

1256.64 

I.II8 

0.04861 

0.8941 

0.980 

1.99131 

1.0200 

1.076 

0.03169 

0.9296 

4i 
42 

1320.25 
I385-44 

•175 
•233 

.07005 
.09098 

.8511 
.8110 

1.030 
.081 

0.01275 
.03368 

0.97II 
.9254 

.130 
.186 

•05313 
.07406 

.8849 
.8432 

43 

1452.20 

.292 

.11142 

•7738 

.133 

.05412 

.8828 

•243 

.09450 

.8044 

44 

1  520.53 

•353 

•I3I39 

•7389 

.186 

.07409 

.8432 

.302 

.11447 

.7683 

45 

1590.43 

1415 

0.15091 

0.7065 

1.241 

0.09361 

0.806  1 

1.361 

0-13399 

0.7345 

46 

1661.90 

479 

.17000 

.6761 

.296 

.11270 

•7714 

423 

•15308 

.7029 

4£ 

1734-94 

•544 

.18868 

.6476 

•353 

•13138 

•7389 

•485 

.17176 

•6734 

48 

49 

1885.74 

.611 
.678 

.20696 
.22487 

.6209 
•5958 

.411 
.471 

.14967 
.16758 

.7085 
.6799 

•549 
.614 

.19005 
.20796 

.6456 
•6i95 

50 

1963.50 

1-748 

0.24242 

0.5722 

1-532 

0.18513 

0.6530 

i.  68  1 

0.22551 

0-595° 

51 
52 

2042.82 
2123.72 

.818 
.890 

.25962 
.27649 

•5500 
.5291 

•593 
•657 

.20232 
.21919 

.6276 
.6037 

& 

•24371 
•25957 

•5705 
•5501 

53 

2206.18 

.964 

.29303 

•5093 

.721 

•23574 

.5811 

.888 

.27612 

•5295 

54 

2290.22 

2.038 

.30927 

.4906 

.786 

•25197 

•5598 

.960 

•29235 

.5101 

55 

2375-83 

2.114 

0.32521 

0.4729 

I.853 

0.26791 

0-5396 

2.034 

0.30829 

0.4917 

SMITHSONIAN  TABLES. 


TABLE  38  (continued). 

METRIC  UNITS. 

Cross  sections  and  weights  of  wires. 


63 


Diam.  in  thou- 
sandths of  a  cm.  1 

Area  of  cross 
section  d*,",)" 

Copper  —  Density  8.90.  , 

Iron  —  Density  7.80. 

Brass—  Density  8.56. 

N 

Log. 

Metres 
per 
Gramme. 

s 

LI 

Log. 

Metres 
per 
Gramme. 

k 

Log. 

iJ 

55 

2375-83 

2.114 

0.32521 

4729 

1.853 

0.26791 

•5396 

2.034 

0.30829 

.4917 

56 

2463.01 

.192 

.34086 

.4562 

.921 

•28356 

•5205 

.108 

•32394 

4743 

57 

255I-76 

.271 

.35623 

4403 

.990 

.29893 

.5024 

.184 

•3393  * 

4578 

58 

2642.08 

•351 

4253 

2.061 

.31404 

.262 

•35442 

.4422 

59 

2733-97 

433 

^38618 

.4112 

.132 

.32889 

.4689 

•340 

•36927 

4273 

60 

2827.43 

2.516 

0.40078 

•3974 

2.205 

0-34349 

4534 

2.420 

0.38387 

.4132 

61 

2922.47 

.601 

4i5J4 

•3845 

.280 

•35784 

4387 

•502 

•39823 

62 

3019.07 

.687 

.42926 

.3722 

•355 

.37196 

.4246 

41235 

.3869 

63 

3117.25 

•774 

.44316 

.3604 

431 

•38587 

4113 

.668 

.42625 

.3748 

64 

3216.99 

.863 

45684 

•3493 

•509 

•39954 

.3985 

,760 

.44092 

•3623 

65 

33l8-3I 

2-953 

0.47031 

•3386 

2.588 

0.41301 

.3864 

2.840 

0.45339 

•3521 

66 

3421.19 

.48357 

.3284 

.669 

.42627 

•3747 

•929 

.46665 

•3415 

67 

3525-65 

.138 

.49663 

•3187 

•750 

43933 

•3636 

3.018 

47971 

•33*3 

69 

3631.68 
3739-28 

'•328 

•5095° 
.52218 

•3094 
•3005 

•833 
.917 

.45220 
.46488 

•3530 
.3429 

.109 

.201 

49258 
•50526 

.3217 
•3I24 

70 

72 

384845 
4071.50 

3.426 

•524 
.624 

0-53479 
•54700 
•55915 

.2919 

.2838 
.2759 

3-003 
.088 
.176 

0.47749 
.48970 
•50185 

•3330 
•3238 
•3*49 

3.295 
485 

0.51787 
•53008 
•54223 

•3°35 

73 

4185.39 

•725 

.57H3 

.2685 

.265 

•51383 

•3063 

•55421 

.2791 

74 

4300.84 

.828 

.58294 

.2612 

•355 

•52565 

.2981 

.682 

•56603 

.2716 

75 

4417-86 

3-932 

0.59460 

•2543 

3446 

0-53731 

.2902 

3.782 

0-57769 

.2644 

76 

4536.46 

4-037 

.60611 

.2477 

.538 

.54881 

.2826 

.883 

.58919 

•2575 

77 

4656.63 

.144 

.61746 

.2413 

.632 

.56017 

•2753 

.986 

.60056 

.2509 

78 
79 

4778.36 
4901.67 

38 

.62867 
•63974 

•2351 
.2292 

.727 
•823 

.57137 
.58244 

.2683 
.2615 

4.090 
•177 

.61175 
.62283 

.2445 
•2394 

80 

5026.55 

4474 

0.65066 

.2235 

3-921 

0.59336 

•2550 

4.303 

0.63375 

.2324 

81 

S'SS-oo 

.586 

.66145 

.2180 

4.019 

.60415 

.2488 

411 

.64454 

.2267 

82 

5281.02 

.700 

.67211 

.2128 

.119 

.61481 

.2428 

•65519 

.2212 

83 

5410.61 

.815 

.68264 

.2077 

.220 

•62534 

•2369 

.631 

.66572 

•2159 

84 

5541-77 

•932 

.69304 

.2027 

-323 

.63574 

•2313 

•744 

.67612 

.2108 

85 

5674-50 

5.050 

0.70332 

.1980 

4.426 

0.64602 

•2259 

4.857 

0.68640 

.2059 

86 

87 
88 
89 

5808.80 
5944-68 
6082.12 
6221.14 

.170 
.291 
413 
•537 

•71348 
•72352 
•73345 
•74326 

•1934 
.1890 

.1847 
.1806 

•531 
-637 

•744 
.852 

.65618 
.66622 
.67615 
.68596 

.2207 

[2108 
.2061 

5'.2o6 
•325 

.69656 
.70660 

•71653 
•72634 

.2OI  I 
.1965 
.1921 
.1878 

90 

6361.73 

5.662 

0.75297 

.1766 

4.962 

0.69567 

.2015 

5.446 

0.73605 

.1836 

91 

6503.88 

.788 

.76256 

.1728 

5-O73 

.70527 

.1971 

.567 

•74565 

.1796 

92 

6647.61 

.916 

.77206 

.1690 

.185 

.71476 

.1929 

.690 

•755*4 

•1757 

93 

6792.91 

6.046 

.78144 

.1654 

.298 

.72414 

.1887 

.815 

•76452 

.1720 

94 

6939.78 

..176 

•79074 

.1619 

413 

•73344 

.1847 

.940 

.77382 

.1683 

95 

7088.22 

6,309 

0.79993 

•1585 

5529 

0.74263 

.1809 

6.068 

0.78301 

.1648 

96 

7238.23 

442 

.80902 

!646 

«75I73 

.1771 

.196 

.79211 

.l6l4 

7389-8i 

•577 

.81802 

.1520 

•764 

•76073 

•1735 

•326 

.80111 

.1581 

99 

7542.96 
7697.69 

•713 
.851 

.82693 
•83575 

.1490 
.1460 

.884 
6.004 

.76964 
.77846 

.1670 
.1665 

457 
.589 

.81002 
.81884 

.1549 
.1518 

100 

7853-98 

6.990 

0.84448 

.I431 

6.126 

0.78718 

.1632 

6.723 

0.82756 

.1487 

SMITHSONIAN  TABLES. 


64 


TABLE  39. 
BRITISH   AND   METRIC   UNITS. 

Cross  sections  and  weights  of  wires. 


The  cross  section  and  the  weight,  in  different  units,  of  Aluminium  wire  of  the  diameters  given  in  the  first  columni 
For  one  tenth  the  diameter  divide  sections  and  weights  by  too.  For  ten  times  the  diameter  multiply  by  100, 
and  so  on. 


Diameter.* 

Area  of 
cross 
section.* 

Aluminium  —  Density  2.67. 

Pounds 
Foot. 

Log. 

Feet 
per 
Pound. 

Ounces 
per 
Foot. 

Log. 

Feet 
per 
Ounce. 

Grammes 
per 

Metre.* 

Log. 

Metres 
per 
Gramme. 

10 

78.54 

.0000909 

5.95862 

1  1  000. 

.001455 

3.16274 

687.5 

.02097 

2.32160 

47.69 

II 

95-°3 

01  1  00 

4.04139 

9091. 

01760 

.24551 

602.4 

•02537 

•40437 

39-41 

12 
13 

113.10 
132.73 

01309 
01536 

.11699 
.18630 

7638. 
6509. 

02095 
02458 

.32111 
.39062 

477-4 
406.8 

.03020 
.03544 

•47997 
.54948 

33-" 

28.22 

1  53-94 

01782 

.25088 

5612. 

02851 

45500 

350.8 

.04110 

.61386 

24.33 

15 

176.71 

.0002045 

4.31079 

4889. 

.003273 

3.51491 

305-6 

.04718 

2-67377 

21.19 

16 

201.06 

02327 

.36685 

4297. 

03724 

.57097 

268.5 

.05368 

.72984 

18.63 

17 

226.98 

•02627 

.41952 

3876. 

04204 

.62364 

237-9 

.06060 

•78250 

16.50 

18 

254-47 

02946 

.46917 

3395- 

04713 

.67329 

212.2 

.06794 

•83215 

14.72 

19 

283-53 

03282 

•S'613 

3047. 

05251 

.72025 

190.4 

.07570 

.87911 

13.21 

20 

314.16 

.0003636 

4.56068 

2750. 

.005818 

3.76480 

I7I.9 

.08388 

2~.92366 

11.922 

21 

346.36 

04009 

.60306 

2494. 

06415 

.80718 

155-9 

.09248 

.96604 

10.813 

22 

380.13 

04400 

.64346 

2273. 

07040 

•84758 

142.0 

.10149 

1.00644 

9-853 

23 

415.48 

04809 

.68208 

2079. 

07697 

.88630 

129.9 

.11093 

.04506 

9.014 

24 

452.39 

05237 

.71904 

1910. 

08378 

.92316 

1194 

.12079 

.08202 

8.279 

25 

490.87 

.0005682 

4-7545° 

1760. 

.00909 

3-95862 

110.00 

.1311 

1.11748 

7.630 

26 

530-93 

06147 

.78867 

1627. 

0983 

.99269 

101.70 

.1418 

•I5I55 

7.054 

27 

572.56 

06628 

•82135 

1509. 

1060 

2-02547 

94-3° 

.1529 

.18433 

6.541 

28 

6i5-75 

07127 

.85293 

1403. 

1140 

.05705 

87.69 

.1644 

.21592 

6.083 

29 

660.52 

07646 

.88341 

1308. 

1223 

•08753 

8i.75 

.1764 

.24640 

5.670 

30 

706.86 

.0008182 

4.91286 

1222. 

.01309 

2.11698 

76.39 

.1887 

1.27584 

5-299 

31 

754-77 

08737 

•94134 

1145- 

1398 

.14546 

71-54 

•2015 

•30433 

4.962 

32 

804.25 

09309 

.96892 

1074. 

1489 

•17304 

66.89 

•2147 

.33*90 

•657 

33 

855.30 

09900 

,-99565 

IOIO. 

'I?4 

.19977 

63-  i  3 

.2284 

.35863 

•379 

34 

907.92 

10509 

3.02158 

952. 

1681 

•22570 

59-47 

.2424 

•38456 

•125 

35 

962.11 

.OOIII4 

3-04675 

897.9 

.01782 

2.25087 

56.12 

•2569 

1.40973 

3.893 

36 

1017.88 

1178 

.07123 

848.8 

1885 

•27535 

53-05 

.2718 

.43421 

.680 

H 

1075.21 
1134.11 

1245 
I3l6 

.09502 
.11918 

803.5 
760.0 

1991 

2105 

.29914 
.32329 

50.22 
47-50 

.2871 
.3035 

.45800 
.48216 

•483 
•295 

39 

1194.59 

1383 

•14075 

723.2 

2212 

•34487 

45-20 

.3190 

•50373 

•135 

40 

1256.64 

.001455 

3-16275 

687.5 

.02327 

2.36687 

42.97 

•3355 

1.52573 

2.980 

41 

1320.25 

1528 

.18419 

6544 

2445 

•38831 

40.90 

•3525 

•54717 

.837 

42 

I385-44 

1604 

.20512 

623.6 

2566 

.40924 

38.97 

•3699 

.56810 

.704 

43 

1452.20 

1681 

•22556 

594-9 

2690 

.42968 

•3877 

•58854 

•579 

44 

1  520.53 

1760 

•24552 

568.2 

28l6 

.44964 

35.51 

.4060 

.6085! 

•463 

45 

1590.43 

.001841 

3.26504 

543-2 

.02946 

"2.46916 

33-95 

.4246 

1.62803 

2-355 

46 

1661.90 

1924 

.28413 

5I9-8 

3078 

.48825 

32-49 

•4437 

.64712 

.254 

47 

1734-94 

2008 

.30281 

498.0 

3213 

•50693 

31.12 

•4632 

.66580 

48 

1809.56 

2095 

.32110 

477-4 

3351 

.52522 

29.84 

.4832 

.68408 

.070 

49 

1885.74 

2183 

•33901 

458.1 

3492 

•54313 

28.63 

•5035 

.70199 

1.986 

50 

1963.50 

.002273 

3-35656 

440.0 

.03636 

2.56068 

27.50 

•5243 

7.71954 

1.907 

Si 
52 

2042.82 
2123-72 

2365 
2458 

•37376 
.39063 

422.9 
406.8 

3783 
3933 

.57788 

•59475 

26.43 
25.42 

•5454 
.5670 

.73674 
.75361 

.833 

53 

2206.18 

2554 

.40717 

394-2 

4086 

.61129 

24.47 

.5891 

.77015 

.698 

54 

2290.22 

2651 

.42341 

377-2 

4242 

•62753 

23-57 

.6115 

.78639 

•635 

55 

-375.83 

.002750 

3-43934 

363-6 

.04400 

2.64346 

22.73 

•6343 

T-80233 

I-576 

*  Columns  3-8,  in  thousandths  of  an  inch  ;  9-12,  thousandths  of  a  centimetre. 
SMITHSONIAN  TABLES. 


TABLE  39  (continued). 

BRITISH   AND   METRIC   UNITS. 

Cross  sections  and  weights  of  wires. 


* 

£ 

Area  of 
cross 
section.* 

Aluminium  —  Density  2.67. 

Pounds 
Foot. 

Log. 

Feet 

per 
Pound. 

Ounces 
per 
Foot. 

Log. 

Feet 
per 
Ounce. 

Grammes 
Metre.* 

Log. 

Metres 
per 
Gramme. 

55 

2375.83 

.002750 

343934 

363.6 

.04400 

2.64346 

22.73 

0.6343 

1.80233 

1-576 

56 

2463.01 

2851 

45500 

350^8 

.04562 

.65912 

21.92 

.606 

.81798 

.521 

57 

255I-76 

2954 

47037 

338.6 

.04726 

.67449 

21.  l6 

.6813 

.83335 

.468 

2642.08 

3058 

.48547 

327.0 

.04893 

.68959 

20.44 

•7054 

.84846 

.418 

59 

2733-97 

3^5 

.50032 

316.0 

•05063 

.70444 

'975 

.7300 

.86331 

•370 

60 

2827.43 

.003273 

3.5I492 

305.5 

.05236 

2.71904 

19.10 

07549 

1.87790 

1.325 

6i 
62 

2922.47 
3019.07 

3383 
3495 

.52928 
•54340 

295.6 
286.2 

.05413 

•05591 

•73340 
•74752 

18.48 
17.88 

& 

.89226 
.90638 

.282 
.241 

63 

3117.25 

3608 

•55730 

277.1 

•05773 

.76142 

17.32 

•8323 

.92028 

.201 

64 

3216.99 

3724 

.57098 

268.5 

.05958 

•77510 

16.78 

8589 

•93396 

.I64 

65 

3318.31 

.003841 

3.58445 

260.3 

.06146 

2.78857 

16.27 

0.8860 

i"-94743 

I.I29 

66 

3421.19 

3960 

•59771 

252.5 

•06336 

.80183 

1578 

•9135 

.96069 

.095 

67 
68 
69 

3525-6J 
3631.68 
3739-28 

4081 
4204 
4328 

.61077 
.62364 
.63632 

245.0 
237.9 
231.0 

.06530 
.06726 
.06925 

.81489 

•82777 
.84044 

14$ 

14.44 

•9413 
.9697 

.9984 

.99930 

.062 
.031 
.OO2 

70 

3848.45 
3959.19 

.004456 
4583 

3-64893 
.66114 

224.4 
218.2 

.07129 
.07333 

2.85305 
.86526 

14.03 
13.64 

1.028 
•057 

0.01191 
.02412 

0.9730 
.9460 

74 

4071.50 
4185.39 
4300.84 

4713 
4845 
4978 

.67328 
.68526 
.69708 

212.2 
206.4 
200-9 

•07541 
•07751 
.07965 

.87740 
.88938 
.90120 

13.26 
12.90 
12.55 

.087 

$ 

.03627 
.04825 
.06006 

.9199 

75 

4417.86 

.005114 

370874 

195-5 

.08182 

2.91286 

12.22 

1.180 

0.07172 

0.8477 

76 

4536.46 
4656.63 
4778.36 

5251 
5390 
5531 

.72025 
.73160 
.74281 

190.4 

185.5 
I80.8 

.08402 
.08624 
.08850 

•92437 
•93572 
.94693 

11.90 

11.60 

11.30 

.211 

.0832.3 
.09458 
.10579 

.8256 
.8043 
7838 

79 

4901.67 

5674 

•75387 

176.2 

.09078 

•95799 

11.02 

.309 

.11686 

j     7641 

80 

5026.55 

.005818 

3-76480 

I7I.9 

•09309 

2.96892 

10.742 

1.342 

0.12778 

07451 

81 

5965 

•77559 

167.6 

.09544 

.97971 

10.479 

.376 

•13857 

.7268 

82 

5281.02 

6113 

.78625 

163.6 

.09781 

.99037 

IO.224 

4IO 

•i  49-23 

.7092 

83 

5410.61 

6263 

.79678 

J597 

.IOO2I 

1.00090 

9-979 

•445 

.15976 

.6922 

84 

5541.77 

6415 

.80718 

155-9 

.10264 

.01130 

9-743 

.480 

.17016 

.6757 

85 

5674-5° 

.006568 

3.81746 

152.2 

.IO5I 

1.02158 

9.515 

!.5iS 

0.18044 

0.6600 

86 

5808.80 

6724 

.82762 

148.7 

.1076 

•03174 

9-295 

•551 

.19060 

.6448 

87 

5944.68 

6881 

•83766 

145-3 

.IIOI 

.04178 

9.082 

•587 

.20064 

.6300 

88 

6082.12 

7040 

.84758 

142.0 

.1126 

•05170 

8.878 

.624 

.21057 

.6158 

89 

6221.14 

7201 

.85740 

138.9 

.1152 

.06152 

8.679 

.661 

.22038 

.6020 

90 

6361-73 

.007364 

3.86710 

135-8 

.1178 

1.07122 

8.488 

1.699 

0.23009 

0.5887 

92 

6503.88 
6647.61 

7528 
7695 

.87670 
.88619 

132.8 
130.0 

.1205 
.1231 

.08082 
.09031 

8.302 

8.122 

•737 
•775 

.23968 
.24918 

•5759 
•5634 

93 

6792.91 

7863 

.89558 

127.2 

.09970 

7-949 

.814 

.25856 

-55H 

94 

6939.78 

8033 

.90487 

124.5 

.I2§5 

.10899 

7.780 

•853 

.26786 

•5397 

95 

7088.22 

.008205 

3.91407 

121.9 

.1313 

1.11819 

7.617 

1.893 

0.27705 

0.5284 

96 

7238.23 

8378 

.92316 

119.4 

•1341 

.12728 

7-459 

•933 

.28614 

7389.81 

8554 

.93216 

116.9 

.1369 

.13628 

7-307 

•973 

.29514 

.5068 

98 

7542.96 

8731 

.94107 

"4-5 

•J397 

•I45I9 

7-I58 

2.014 

•30405 

•4965 

99 

7697.69 

8910 

.94989 

1  1  2.2 

.1426 

.15401 

•055 

.31287 

.4865 

100 

7853.98 

.009091 

3.95862 

IIO.O 

•1455 

1.16274 

6.875 

2.097 

0.32160 

0.4769 

*  Columns  3-8,  in  thousandths  of  an  inch;  9-12,  thousandths  of  a  centimetre. 
SMITHSONIAN  TABLES. 


66 


TABLE  40. 

SIZE,  WEIGHT,  AND   ELECTRICAL 

Size,  Weight,  and  Electrical  Constants  of  pure  hard  drawn  Copper  Wire  of  different  numbers 
Size  and  Weight 


Gauge 
Number. 

Diameter  in 
Inches. 

Square  of 
Diameter 
(Circular 
Inches). 

Section  in 
Sq.  Inches. 

Pounds 

Log. 

Feet 
per 
Pound. 

OOOO 

0.4600 

0.21  l6 

0.1662 

0.6412 

1.80701 

1.560 

000 

.4096 

.1678 

.1318 

.5085 

.70631 

1.967 

00 

.3648 

.1331 

.1045 

.4033 

.60560 

2.480 

0 

•3249 

•1055 

.0829 

•3«98 

.50489 

3.127 

1 

0.2893 

0.08369 

0-06573 

0.2536 

1.40419 

3-943 

2 

.2576 

.06637 

.05213 

.2OI  I 

.30348 

4.972 

3 

.2294 

.05263 

.04134 

•1595 

.20277 

6.270 

4 

.2043 

.04174 

•03278 

.1265 

.10206 

7-905 

5 

.1819 

.03310 

.02000 

.1003 

.00136 

9.969 

6 

7 

0.1620 
•1443 

0.02625 
.02082 

0.02062 
•01635 

0.07955 
.06309 

2.90065 
.79994 

12.57 
I5-85 

8 

.1285 

.01651 

.01297 

.05003 

.69924 

19.99 

9 

.1144 

.01309 

.01028 

.03968 

.59853 

25.20 

10 

.1019 

.01038 

.00815 

.03146 

.49782 

3I-78 

11 

0.00074 

0.008234 

0.006467 

0.02495 

2.39711 

40.08 

12 

.08081 

.006530 

.005129 

.01979 

.29641 

50-54 

13 

.07196 

.005178 

.004067 

.01569 

.19570 

63-72 

14 

.06408 

.004107 

.003225 

.01244 

.09499 

80.35 

15 

•05707 

.003257 

.002558 

.00987 

3.99429 

101.32 

16 

0.05082 

0.002583 

O.OO2O28 

0.007827 

3-89358 

127.8 

17 

.04526 

.002048 

.001609 

.006207 

.79287 

161.1 

18 

.04030 

.001624 

.001276 

.004922 

.69217 

203.2 

19 

.03589 

.001288 

.OOIOI2 

.003904 

.59146 

256.2 

20 

.03196 

.001021 

.000802 

.003096 

.49075 

323-1 

21 

0.02846 

O.OOOSlOI 

0.0006363 

0.002455 

3-39004 

408.2 

22 

•02535 

.0006424 

.0005046 

.001947 

•28934 

5I3-6 

23 

.02257 

.0005095 

.0004001 

.001544 

.18863 

647.7 

24 

.O2OIO 

.0004040 

.0003173 

.001224 

.08792 

816.7 

25 

.01790 

.0003204 

.0002517 

.000971 

4.98722 

1029.9 

26 

0.01594 

0.0002541 

0.0001996 

O.O007700 

4.88651 

1298. 

3 

.01419 
.01264 

.0002015 
.0001598 

.OOOI  583 
.0001255 

.0006107 
.0004843 

.78580 
.68510 

1638. 
2065. 

29 

.OII26 

.0001267 

.0000995 

.0003841 

.58439 

2604. 

30 

.01003 

.0001005 

.0000789 

.0003046 

.48368 

3283- 

31 

0.008928 

O.OOOO797O 

0.00006260 

0.0002415 

4.38297 

4140. 

32 

.007950 

.0000632! 

.00004964 

.0001915 

.28227 

5221. 

33 
34 

.007080 
.006304 

.OOOO5OI3 
.00003975 

.00003937 
.00003122 

.0001519 
.OOOI2O5 

.18156 
.08085 

6583. 
8301. 

35 

.005614 

.00003152 

.00002476 

.0000955 

5.98015 

10468. 

36 

O.005000 

O.OOOO25OO 

O.OOOOIOJ53 

0.00007576 

5-87944 

13200. 

37 

.004453 

.00001983 

.00001557 

.00006008 

.77873 

16644. 

38 

.003965 

.00001372 

.00001235 

.00004765 

.67802 

20988.  * 

39 

40 

.003531 
.003145 

.00001247 
.00000989 

.OOOOO979 
.00000777 

.00003778 
.00002996 

•57732 
.47661 

26465. 
33372. 

SMITHSONIAN  TABLE*. 


TABLE  40  (continued). 
CONSTANTS  OF  COPPER  WIRE. 

according  to  the  American  Brown  and  Sharp  Gauge.    Common  Measure.    Temperature  32°  F.    Density  8.90. 

Electrical  Constants 


67 


Resistance  and  Conductivity. 

Gauge 
Number. 

Ohms 
per 
Foot. 

Log. 

Feet 
per 
Ohm. 

Ohms 
per 
Pound. 

Pounds 
per 
Ohm. 

0.00x504629 

S-6655I 

2l6oi. 

0.00007219 

13852. 

0000 

.00005837 
.00007361 
.00009282 

.76622 
.86693 
.96764 

17131. 
13586. 
10774. 

.00011479 
.00018253 
.00029023 

8712. 

5479- 
3445- 

000 

00 
0 

0.0001170 

4-06834 

8544. 

0.0004615 

2166.8 

1 

.0001476 

.16905 

6775- 

.0007338 

1362.8 

2 

.000l86l 

.26976 

5373- 

.0011668 

857.0 

3 

.0002347 

.37046 

4261. 

.0018552 

539-0 

4 

.0002959 

.47117 

3379- 

.0029499 

339-0 

5 

0.0003731 

4.57188 

2680. 

0.004690 

213.22 

6 

.0004705 
.0005933 
.0007482 

.67259 

.77329 
.87400 

2125. 
1685. 
r337. 

.007458 
.011859 
.018857 

134-08 
84.32 
53.03 

I 

9 

.0009434 

.97471 

1060. 

.029984 

33-35 

10 

O.OOII90 
.001500 
.001892 

3-0754I 
.17612 
.27683 

840.6 
666.6 
528.7 

0.04768 
.07581 
.12054 

20.973 

Is 

11 

12 
13 

.002385 

•37753 

419.2 

.19166 

5.218 

14 

.003000 

.47824 

332.5 

.30476 

3.281 

IS 

0.003793 

3.57895 

263.7 

0.4846 

2.0636 

16 

.004783 
.006031 

.78036 

209.1 
165.8 

.7705 
1.2252 

1.2979 
0.8162 

11 

.007604 
.009589 

.88107 
.98178 

^•S 
104.3 

1.9481 
3.0976 

.3228 

'9 

20 

O.OI209 
.01525 

2.08248 
.18319 

82.70 
65-59 

4.925 
7.832 

0.20305 
.12768 

21 

22 

.01923 

.28390 

52.01 

12.453 

.08030 

23 

.02424 

.38461 

41.25 

19.801 

.05051 

24 

•03057 

•48531 

32.71 

31.484 

.03176 

2S 

0.03855 

2.58602 

25.94 

50.06 

0.019976 

26 

.04861 

.68673 

20.57 

79.60 

.012563 

27 

.06130 

.78743 

16.31 

126.57 

.007901 

28 

.07729 

.88814 

12.94 

2OI.2O 

.004969 

29 

.09746 

.98885 

10.26 

320.01 

.003125 

30 

0.1229 

.1550 

1.08955 
.19026 

8.137 
6.452 

g? 

0.0019654 
.0012359 

31 

32 

•J954 

.29097 

5-"7 

1286.5 

.0007773 

33 

.2464 

.39168 

4.058 

2045.6 

.0004889 

34 

•3107 

.49238 

3.218 

3252.6 

.0003074 

35 

0.3918 

.4941 

7.59309 
.69380 

2.552 
2.024 

8224! 

0.0001934 
.0001216 

36 

37 

s 

.6230 
.7856 

•79450 
.89521 

1.605 
1.273 

13076. 
20792. 

.0000765 
.0000481 

38 
39 

.9906 

.99592 

1.009 

33060. 

.0000303 

40 

SMITHSONIAN  TABLES. 


68 


TABLE  41 . 

SIZE,  WEIGHT,  AND   ELECTRICAL 

Size,  Weight,  and  Electrical  Constants  of  pure  hard  drawn  Copper  Wire  of  different  numbers 
Size  and  Weight. 


Gauge 
Number. 

Diameter  in 
Centimetres. 

Square  of 
Diameter 
(Circular 
Cms.). 

Section  in 
Sq.  Cms. 

Grammes 
Metre. 

Log. 

Metres 
per 
Gramme. 

0000 
000 

1.1684 
.0405 

1.3652 

.0826 

1.0722 
0-8503 

m 

2.97966 
.87896 

0.001048 
.001322 

00 

o 

£25! 

0.8586 
.6809 

.6743 
•5348 

600.  1 
475-9 

.77825 
•67754 

.001666 
.002  1  OI 

1 

0.7348 

0.5400 

0.4241 

377-4 

2.57684 

O.002649 

2 

3 

.6^44 

.4282 

5$ 

299-3 

2^74 

•47613 
•37542 

.003341 
.004213 

4 

'.5189 

.2693 

.2115 

188.2 

.27472 

.005312 

5 

.4621 

.2136 

.1677 

149-3 

.17401 

.006699 

6 

0.4115 

0.16936 

0.13302 

118.39 

2.07330 

0.00845 

8 

.3665 
.3264 

•'3431 
.10651 

.10549 
.08366 

93.88 
74-45 

1.97259 
.87189 

.01065 
•01343 

9 

.2906 

.08447 

.06634 

59-04 

.77118 

.01694 

10 

.2588 

.06699 

.05261 

46.82 

.67047 

.02136 

11 

0.2305 

0.05312 

0.04172 

37.13 

I-56977 

0.02693 

12 

13 

.2053 
.1828 

.04213 
•03341 

•03309 
.02624 

29-45 
23-35 

•36835 

•03396 
.04282 

14 
15 

.1628 
.1450 

.02649 

.02IOI 

.02081 
.01650 

18.52 
14.69 

.26764 
.16694 

.05400 
.06809 

16 

0.12908 

0.016663 

0.013087 

11.648 

1.06623 

0.0859 

17 

.H495 

.013214 

.010378 

9-237 

0.96552 

.1083 

18 

.10237 

.010479 

.008231 

7-325 

.86482 

•1365 

19 

20 

.09116 
.08118 

.008330 
.006591 

.006527 
.005176 

5.809 
4.607 

•764" 
.66340 

.1721 
.2171 

21 

0.07229 

0.005227 

0.004105 

3-653 

0.56270 

0.2737 

22 

.06438 

.004145 

•003255 

2.898 

.46199 

.3450 

23 
24 

•05733 
.05106 

.003287 
.002607 

.002582 
.002047 

2.298 
1.822 

.36128 
•26057 

25 

•04545 

.002067 

.001624 

I«445 

•15987 

.6920 

26 

0.04049 

0.0016394 

0.0012876 

1.1459 

0.05916 

0.873 

27 

.03606 

.0013001 

.001  02  1  1 

.9088 

1.95845 

1.  100 

28 

.03211 

.0010310 

.0008098 

.7207 

.85775 

1.388 

29 

.02859 

.0008176 

.0006422 

.5715 

.75704 

1.750 

30 

.02546 

.0006484 

.0005093 

•4532 

•65633 

2.206 

31 

32 

0.02268 
.02019 

O.OOO5I42 
.0004078 

0.0004039 
.0003203 

0-3594 
.2850 

I.55562 
.45492 

2.782 
3.508 

33 

.01798 

.0003234 

.0002540 

.2261 

•35421 

4.424 

34 

35 

.01601 
.01426 

.0002565 
.OOO2O34 

.0002014 
.0001597 

•T793 
.1422 

•25350 
.15280 

5-578 
7-034 

36 

0.01270 

0.000l6l3 

0.0001267 

0.1127 

1.05209 

8.87 

37 

.01131 

.OOOI  279 

.0001005 

.0894 

2.95138 

11.18 

38 

.01007 

.OOOIOI4 

.0000797 

.0709 

.85068 

14.10   ' 

39 

.00897 

.0000804 

.0000632 

.0562 

•74997 

17.78 

40 

.00799 

.0000638 

.0000501 

.0446 

.64926 

22.43 

SMITHSONIAN  TABLES. 


TABLE  41  (.continued}. 

CONSTANTS  OF  COPPER   WIRE. 

according  to  the  American  Brown  and  Sharp  Gauge.    Metric  Measure.    Temperature  o°  C.    Density  8.90. 

Electrical  Constants. 


Resistance  and  Conductivity. 

Number. 

Ohms 
Metre. 

Log. 

Metres 
per 
Ohm. 

Ohms 
per 
Gramme. 

Grammes 
Ohm. 

0.0001519 

4.18150 

6584. 

0.0000001592 

6283000. 

0000 

.0001915 

.28221 

5221. 

.0000002531 

3951000. 

ooo 

.0002415 

.38191 

4141. 

.0000004024 

2485000. 

00 

.0003045 

•48362 

3284- 

.0000006398 

1563000. 

o 

0.0003840 

4.58433 

2604. 

O.OOOOOIOI7 

982900. 

1 

.0004842 

.68503 

2065. 

.000001618 

618200. 

2 

.0006106 

78574 

1638. 

.000002572 

388800. 

3 

.0007699 
.0009709 

.88645 
.98715 

1299. 
1030. 

.000004090 
.000006504 

244500. 
153800. 

4 
5 

0.001224 

3.08786 

816.9 

O.OOOOIO34 

96700. 

6 

.001544 

.18857 

647-8 

.00001644 

60820. 

7 

.001947 

.28928 

5^3-7 

.00002615 

38250. 

8 

.002455 

.38998 

407.4 

.00004157 

24050. 

9 

.003095 

.49069 

323.1 

.00006610 

I5I30. 

10 

0.003903 

3.59140 

256.2 

O.OOOI05II 

9514. 

11 

.004922 

.69210 

203.2 

.00016712 

598* 

12 

.006206 

.79281 

161.1 

.00026574 

3763. 

13 

.007826 

.89352 

127.8 

.00042254 

2367. 

14 

.009868 

.99423 

101.3 

.00067187 

1488. 

13 

0.01244 

2.09493 

80.37 

0.0010683 

936.1 

16 

.01569 

.19564 

63-73 

.0016987 

588.7 

ll 

.01979 

'29635 

50-54 

.0027010 

370.2 

18 

.02495 

.39705 

40.08 

.0042948 

232.8 

19 

.03146 

.49776 

31-79 

.0068290 

146.4 

20 

0.03967 

2.59847 

25.21 

0.010859 

92.09 

21 

.05002 

.69917 

19.99 

.017266 

57.92 

22 

.06308 

.79988 

I5-85 

.027454 

36.42 

23 

•07954 

^90059 

12-57 

.043653 

22.91 

24 

.10030 

1.00130 

9-97 

.069411 

11.88 

25 

0.12647 

T.IO2OO 

7.907 

O.II037 

9.060 

26 

.15948 

.20271 

6.270 

.17549 

5.698 

27 

.201  10 

•30342 

4-973 

.27904 

3-584 

28 

.25358 

.40412 

3-943 

.44369 

2.254 

29 

.31976 

.50483 

3.127 

.70550 

1.417 

30 

0.4032 

1.60554 

2.480 

I.I2I8 

0.8914 

31 

.5084 

.70624 

1.967 

1.7837 

.5606 

32 

.6411 

.80695 

1.560 

2.8362 

.3526 

33 

.8085 

.90766 

1.237 

4.5097 

.2217 

34 

I.OI94 

0.00837 

0.981 

7.1708 

•1394 

35 

1-2855 

0.10907 

0.7779 

11.376 

0.08790 

36 

I.62IO 

.20978 

.6169 

18.130 

.05516 

37 

2.0440 

.31049 

.4892 

28.828 

.03469 

38 

2-5775 

.41119 

.3880 

45.838 

.02182 

39 

3.250I 

.51190 

.3076 

72.885 

.01372 

40 

SMITHSONIAN  TABLES. 


JO 


TABLES  42-43. 
WEIGHT  OF  SHEET  METAL. 


TABLE  42.  -  Weight  of  Sheet  Metal.    (Metric  Measure.) 

This  table  gives  the  weight  in  grammes  of  a  plate  one  metre  square  and  of  the  thickness  stated  in  the 

first  column. 


Thickness 

in  thou- 
sandths of 

Iron. 

Copper. 

Brass. 

.A  1  u  m  i  n  u  m  • 

Platinum. 

Gold. 

Silver. 

a  cm. 

1 

78.0 

89.0 

85.6 

26.7 

215.0 

193.0 

105.0 

2 

3 

156.0 
234.0 

178.0 
267.0 

171.2 
256.8 

£1 

430.0 
645-0 

386.0 
579-0 

2IO.O 
3I5-0 

4 

312.0 

356.0 

342.4 

1  06.8 

860.0 

772.0 

420.0 

5 

390.0 

445-0 

428.0 

133-5 

1075.0 

965.0 

525-0 

6 

468.0 

534-0 

5'3.6 

160.2 

1290.0 

1158.0 

630.0 

7 

546.0 

623.0 

599-2 

186.9 

1505.0 

1351.0 

735-0 

8 

624.0 

712.0 

684.8 

213.6 

1720.0 

1544.0 

840.0 

9 

10 

702.0 
780.0 

801.0 
890.0 

770.4 
856.0 

240.3 
267.0 

1935-0 
2150.0 

1737.0 
1930.0 

945-0 
1050.0 

TABLE  43.  -Weight  of  Sheet  Metal.    (British  Measure.) 


Thickness 
in  Mils. 


9 

10 


Iron. 


Pounds  per 
Sq.  Foot. 


.04058 
.08116 
.12173 
.16231 
.20289 

•24347 
.28405 

-32463 
.36520 
.40578 


Copper. 


Pounds  per 
Sq.  Foot. 


.04630 
.09260 

.1    ~ 


.15520 
•23150 

.27780 
.32411 

•37041 
.41671 
.46301 


Brass. 


Pounds  per 
Sq.  Foot. 


.04454 
.08908 

.13363 
.17817 
.22271 

.26725 

•3"  79 


.4 
.44542 


Aluminum. 


Pounds  per 
Sq.  Foot. 


.01389 
.02778 
.04167 
•05556 
.06945 

•08334 
.09723 

.11112 

.12501 
.13890 


Ounces  per 
Sq.  Foot. 


.2222 

•4445 
.6667 
.8890 

I.III2 


1-3335 

1-5557 
1.7780 

2.OOO2 
2.2224 


Platinum. 


Pounds  per 
Sq.  Foot. 


.1119 
.2237 
.3356 

-4474 
•5593 

.6711 


1.0067 

1.1185 


Ounces  per 
Sq.  Foot. 


1.790 
3-579 


7.158 
8.948 

10.738 

12.527 

'4-317 
16.106 
17-896 


Thickness 
in  Mils. 


1 

2 

3 

4 
5 

6 

I 

9 

10 


Gold. 


Troy 

Ounces  per 
Sq.  Foot. 


1.4642 
2.9285 
4.3927 
5.8570 
7.3212 

8.7854 
10.2497 

"•7139 
13.1782 
14.6424 


Grains  per 
Sq.  Foot. 


702.8 

2108.5 
2811.3 
35M-2 

4217.0 
4919.8 
5622.7 

6323-5 
7028.3 


Silver. 


Troy 

Ounces  per 
Sq.  Foot. 


0.7967 
1-5933 
2-: 
3-U 


4.7800 
5-5767 
6.3734 
7.1700 
7.9667 


Grains  per 
Sq.  Foot. 


382.4 

764.8 

1147.2 

1529.6 

1912.0 

2294.4 
2676.8 
3059-2 
3441.6 
3824.0 


SMITHSONIAN  TABLES. 


TABLE  44. 
STRENGTH  OF  MATERIALS. 


The  strength  of  most  materials  varies  so  that  the  following  figures  serve  only  as  a  rough  indication  of  the  strength  of  a 

particular  sample. 


TABLE  44 (a). -Metals. 


TABLE  44(1)).  — Stones.* 


Name  of  Metal. 

Tensile  strength  in 
pounds  per  sq.  in. 

Material. 

Size  of  test 
piece. 

Resistance  to 
crushing  in 
pds.  per  sq.in. 

Aluminum  wire 
Brass  wire 
Bronze  wire,  phosphor,  hard- 
drawn 
Bronze    wire,    silicon,   hard- 
drawn 
Bronze  :  Cu,  58.54  parts  ;  Zn, 
38.70;  Al,  0.21;  with  2.55 
parts  of  the  alloy,  Sn,  29.03, 
wrought  iron,  58.06,  ferro- 
manganese,  12.91 
Copper  wire,  hard-drawn 
Gold  wire 
Iron,  cast 
"     wire,  hard-drawn 
"        "      annealed 
Lead,  cast  or  drawn 
Palladium  * 
Platinum  *  wire 
Silver  *  wire 
Steel 
"  wire,                   maximum 
"  Specially  treated  nickel- 
steel,  approx.  com  p.  0.40 
C  ;    3.25  Ni  ;   treatment 
secret 
"  piano     wire,    0.033     in. 
diam. 
"  piano  wire,  0.051  in.  diam. 
Tin,  cast  or  drawn 
Zinc,  cast 
"    drawn 

3OOOO-4OOOO 
50000-150000 

IIOOOO-I4OOOO 
95000-II5000 

60000-75000 
60000-70000 
2OOOO 
I3OOO-33OOO 
8OOOO-I2OOOO 
5OOOO-6OOOO 
2600-3300 
39000 
5OOOO 
42OOO 
80000-330000 
400000 

250000 

357000-390000 
325000-337000 
4000-5000 
7000-13000 
22OOO-3OOOO 

Marble 
Tufa 
Brownstone 
Sandstone 
Granite 
Limestone 

4  in.  cubes 

2   "        " 

4  in.  cubes 
4«      - 
4«      « 

7600-20700 
77OO-Il6oo 
7300-23600 
2400-29300 
9700-34000 
6000-25000 

*  Data  furnished  by  the  U.  S.  Geological  Survey. 
TABLE  44(0).  -Brick.* 

Kind  of  Brick. 

Resistance  to  crushing  in  pds. 
per  sq.  in. 

Tested 
flatwise. 

Tested 
on  edge. 

Soft  burned 
Medium  burned 
Hard  burned 
Vitrified 
Sand-lime 

1800-4000 
4000-6000 
6000-8500 
8500-25000 
1800-4000 

1600-3000 
3000-4500 
4500-6500 
6500-20000 

4| 

According  to  Boys,  quartz  fibres  have  a 
tensile  strength  of  between  116000  and  167000 
pounds  per  square  inch. 

Brick  piers  laid  up  in  i  part  Portland 
cement,  3  of  sand,  have  from  20  to  40  per 
cent  the  crushing  strength  of  the  brick. 

*  Authority  of  Wertheim. 


*  Data  furnished  by  the  U.  S.  Geological  Survey. 


TABLE  44  (d).- Concretes.* 


Coarse  material. 
"  Aggregate." 

Proportions  by  volume. 
Cement  :  sand  :  aggregate. 

Size  of  test  piece. 

Resistance  to 
crushing  in  pds. 
per  sq.  in. 

Sandstone 
Cinders 
Limestone 
Conglomerate 
Trap 

1  :  5  :  14  to       :  I  :  5 
1:3:6      "        :  I  :  3 
1:4:8      "       :  2  :  4 
I  :6  :  12    "        :  2  :4 
1:3:9      "        :  2  :  4 

12  in.  cube 

12  "        " 
12   "        " 
12   "        " 
12   "        « 

1550-3860 
790-2050 
1200-2840 
1080-3830 
820-2960 

*  Data  furnished  by  the  U.  S.  Geological  Survey. 
SMITHSONIAN  TABLES. 


72  TABLE  45. 

STRENGTH  OF  MATERIALS. 

Average  Results  of  Timber  Tests. 

The  test  pieces  were  SMALL  and  SELECTED.  Endwise  compression  tests  of 
some  of  the  first  lot,  made  when  green  and  containing  over  40  per  cent  moisture, 
showed  a  diminishing  in  strength  of  50  to  75  per  cent. 

See  also  Table  46.  A  particular  sample  may  vary  greatly  from  these  data, 
which  can  indicate  only  in  a  general  way  the  relative  values  of  a  kind  of  timber. 
Note  that  the  data  below  are  from  selected  samples  and  therefore  probably  high. 

The  upper  lot  are  from  the  U.  S.  Forestry  circular  No.  15  ;  the  lower  from  the 
tests  made  for  the  loth  U.  S.  Census. 


TRANSVERSE 
TESTS. 

COMPRESSION. 

SHEAR- 
ING. 

NAME  OF  SPECIES. 

Modulus 
of  rupture. 
Ib./sq.  in. 

Modulus  of 
elasticity. 
Ibs./sq.  in. 

|  to  grain. 
Ibs./sq.  in. 

J_  to  grain. 
Ibs./sq.  in. 

Along  the 
gram. 
Ibs./sq.  in. 

Long-leaf  pine 

12,600 

2,070,000 

8,000 

I26o 

835 

Cuban  pine 

13,600 

2,370,000 

8,700 

1200 

770 

Short-leaf  pine 
Loblolly  pine 

10,100 
11,300 

1,680,000 
2,050,000 

6,500 
7,400 

1050 
1150 

770 
800 

White  pine 

7,900 

1,390,000 

5,400 

700 

4OO 

Red  pine 

9,100 

I,62O,OOO 

6,700 

IOOO 

500 

Spruce  pine 

IO,OOO 

1,640,000 

7,300 

I2OO 

Boo 

Bald  cypress 

7,900 

1,290,000 

6,OOO 

800 

500 

White  cedar 
Douglass  spruce 

6,300 
7,900 

9IO,OOO 
1,680,000 

5,200 

5,700 

700 
800 

400 
500 

White  oak 

I3,IOO 

2,090,000 

8,500 

2200 

IOOO 

Overcup  oak 
Post  oak 

11,300 
12,300 

I,62O,OOO 
2,030,000 

7,300 

7,100 

lOXX) 
3000 

IOOO 
IIOO 

Cow  oak 

11,500 

I,6lO,000 

7,400 

I9OO 

900 

Red  oak 

11,400 

1,970,000 

7,200 

2300 

IIOO 

Texan  oak 

13,100 

I,86o,OOO 

8,100 

2OOO 

900 

Yellow  oak 

IO,8OO 

1,740,000 

7,300 

I800 

IIOO 

Water  oak 

12,400 

2,000,000 

7,800 

2000 

IIOO 

Willow  oak 

10,400 

1,750,000 

7,200 

IOOO 

900 

Spanish  oak 

I2,OOO 

1,930,000 

7,700 

I800 

900 

Shagbark  hickory 
Mockernut  hickory 

16,000 
15,200 

2,390,000 
2,320,000 

9,500 

10,100 

2700 
3100 

IIOO 
IIOO 

Water  hickory 

12,500 

2,o8o,000 

8,400 

2400 

IOOO 

Bitternut  hickory 

15,000 

2,280,000 

9,600 

22OO 

IOOO 

Nutmeg  hickory 

12,500 

1,940,000 

8,800 

2700 

IIOO 

Pecan  hickory 

15,300 

2,530,000 

9,100 

2800 

1200 

Pignut  hickory 

18,700 

2,730,000 

10,900 

3200 

1200 

White  elm 

10,300 

1,540,000 

6,500 

I2OO 

800 

Cedar  elm 

13,50° 

1,700,000 

8,000 

2100 

1300 

White  ash 

10,500 

1,640,000 

7,200 

1900 

IIOO 

Green  ash 

11,600 

2,050,000 

8,000 

I7OO 

IOOO 

Sweet  gum 

9,5oo 

1,700,000 

7,100 

1400 

800 

Poplar 

9,400 

1,330,000 

5,000 

1120 

Basswood 

8,340 

1,172,000 

5,190 

880 

Ironwood 

7.540 

1,158,000 

5,275 

2000 

Sugar  maple 
White  maple 

16,500 
14,640 

2,250,000 
I,8oo,000 

8,800 
6,850 

3000 
2580 

Box  elder 

873,000 

4,580 

1580 

Black  walnut 

11,900 

1,560,000 

8,000 

2680 

Sycamore 

7,000 

790,000 

6,400 

2700 

Hemlock 

9,480 

1,138,000 

5,400 

IIOO 

Red  fir 

13,270 

1,870,000 

7,780 

1750 

Tamarack 

13,150 

1,917,000 

7,400 

1480 

Red  cedar 

1  1,  800 

938,000 

6,300 

2000 

Cottonwood 

10,440 

1,450,000 

5,ooo 

IIOO 

Beech 

16,200 

1,730,000 

6,770 

2840 

SMITHSONIAN  TABLES. 


TABLE  46. 


UNIT  STRESSES   FOR    STRUCTURAL   TIMBER    EXPRESSED   IN 
POUNDS  PER  SQUARE  INCH. 

Recommended  by  the  Committee  on  Wooden  Bridges  and  Trestles,  American  Railway 
Engineering  Association,  1909. 


BENDING. 

SHEARING. 

KIND  OF  TIMBER. 

Extreme  fibre 
stress. 

Modulus  of 
elasticity. 

Parallel  to  grain. 

Longitudinal 
shear  in  beams. 

Average 
ultimate. 

Safe 
stress. 

Average. 

Average 
ultimate. 

Safe 
stress. 

Average 
ultimate. 

Safe 
stress. 

Douglass  fir 

6lOO 

1200 

,510,000 

690 

170 

270 

no 

Long-leaf  pine 

6500 

1300 

,010,000 

720 

1  80 

300 

1  20 

Short-leaf  pine 

5600 

IIOO 

,480,000 

710 

170 

330 

130 

White  pine 

4400 

900 

,130,000 

400 

100 

180 

70 

Spruce 
Norway  pine 

4800 
420O 

1000 
800 

,310,000 
,190,000 

600 
590 

ISO 
130 

170 

70 

100 

Tamarack 

4600 

900 

,220,000 

670 

170 

260 

100 

Western  hemlock 

5800 

IIOO 

,480,000 

630 

160 

270* 

100 

Redwood 

5000 

900 

8OO,OOO 

300 

80 

- 

- 

Bald  cypress 
Red  cedar 

4800 
4200 

1,150,000 
860,000 

500 

120 

; 

— 

White  oak 

5700 

IIOO 

1,150,000 

840 

210 

270 

no 

COMPRESSION. 

J.4 

KIND  OF  TIMBER. 

Perpendicular 
to  grain. 

Parallel  to  grain. 

l.si 

Formulas  for  safe 

K 

stress  in  long 

0  & 

U    **   V 

columns  over  15 

.9  cP 

Elastic 

Safe 

Average 

Safe 

o  «*« 

diameters.  t 

3'£ 

limit. 

stress. 

ultimate. 

stress. 

*'§  ^ 

K  <» 

9 

Douglass  fir 
Long-leaf  pine 
Short-leaf  pine 

630 
520 
340 

3JO 

260 
170 

3600 
3800 
3400 

1200 
1300 
IIOO 

900 
830 

I200(l-L/6o.D) 

i3oo(i-L/6o.D) 
noo(i-L/6o.D) 

10 
10 
10 

White  pine 

290 

150 

3000 

1000 

7  So 

iooo(i-L/6o.D) 

IO 

Spruce 
Norway  pine 
Tamarack 

370 

180 

150 
220 

3200 
2600* 
3200* 

IIOO 
800 
IOOO 

830 
600 
75° 

noo(i-L/6o.D) 
8oo(i-L/6o.D) 
iooo(i-L/6o.D) 

- 

Western  hemlock 

440 

220 

35°° 

I2OO 

900 

i20o(i-L/6o.D) 

- 

Redwood 

400 

I5° 

3300 

900 

680 

9oo(i-L/6o.D) 

- 

Bald  cypress 
Red  cedar 
White  oak 

340 
470 
920 

170 
230 
450 

3500 

IIOO 

900 
1300 

830 
680 
980 

iioo(i-L/6o.D) 
90o(i-L/6o.D) 
i30o(i-L/6o.D) 

12 

These  unit  stresses  are  for  a  green  condition  of  the  timber  and  are  to  be  used  without  increasing  the  live- 
load  stresses  for  impact. 


SMITHSONIAN  TABLES. 


*  Partially  air-dry. 

t  L= length  in  inches.    D  =  least  side  in  inches. 


74 


TABLES  47-47A. 
ELASTIC  MODULI, 


TABLE  47.  -  Rigidity  Modulus. 

If  to  the  four  consecutive  faces  of  a  cube  a  tangential  stress  is  applied,  opposite  in  direction  on 
adjacent  sides,  the  modulus  of  rigidity  is  obtained  by  dividing  the  numerical  value  of  the  tangential 
stress  per  unit  area  (kg.  per  sq.  mm.)  by  the  number  representing  the  change  of  angles  on  the 
non-stressed  faces,  measured  in  radians. 


Substance. 

Rigidity 
Modulus. 

Refer- 

ence. 

Substance. 

Rigidity 
Modulus. 

Refer- 
ence. 

335° 

25»0 
3550 
3715 
3700 
1240 
4060 
2450 
4780 
4213 
445° 
4664 
2850 

3950 
5210 
6706 

7975 
6940 
8108 

7505 
1710 
7820 
4359 

H 

5 
10 
ii 
5 
5 
5 

J 

10 
19 
5 
14 

5 
15 

10 

I 

14 
5 
5 
ii 

Quartz  fibre    .         . 

2888 
2380 
2960 
2650 
2566 
2816 
8290 

7458 
8070 
7872 
173° 
1543 
3880 
3820 
6630 
6220 

2350 
2730 
1770 
1280 
1190 
2290 

2O 
21 

5 
10 
16 
ii 
16 
15 
5 
ii 

5 
19 

5 

J? 
16 

22 

23 
23 
23 
23 

«            «< 

Brass     

Silver     

M 

<t 

"     cast,  ooCu-f  12  Sn    . 
Bismuth,  slowly  cooled    .    . 
Bronze,  cast,  88  Cu  +  12  Sn  . 
Cadmium,  cast    

« 

"      hard-drawn  .... 
Steel  

"    cast                           .    . 

"    cast,  coarse  gr.    .    .    . 

<i 

« 

Tin,  cast         .... 

« 

U 

Gold  

Zinc  .  '  

u 

ft 

Iron,  cast   ....... 

« 

« 

M 

Glass     

« 

M 

M 

Clay  rock   

N 

Granite  .              ..... 

Magnesium,  cast     .... 
Nickel    

Marble  

Slate      ........ 

Phosphor  bronze     .... 

References  1-16,  see  Table  48.                              21  Boys,  Philos.  Mag.  (5)  30,  1890. 
17  Gratz,  Wied.  Ann.  28,  1886.                             22  Thomson,  Lord  Kelvin. 
18  Savart,  Pogg.  Ann.  16,  1829.                            23  Gray  and  Milne. 
19  Kiewiet,  Diss.  Gottingen,  1886.                       24  Adams-Coker,  Carnegie  Publ.  No.  46, 
20  Threlfall,  Philos.  Mag.  (5)  30,  1890.                          1906. 

TABLE  47a.  —Variation  of  the  Rigidity  Modulus  with  the  Temperature. 
nt  =  n0  (i  —  of  —  &f2  —  7/3),  where  /  =  temperature  Centigrade. 


Substance. 

n0 

aio« 

* 

? 

Authority. 

Brass    .    .    . 

2652 
3200 
3972 

^ 
8108 

6940 
6632 
2566 
8290 

2158 

455 
2716 

57J 
206 
483 
in 

387 
187 

48 
36 

19 

12 

5° 
38 
59 

32 
47 
—  ii 

—8 
ii 
—9 

Pisati,  Nuovo  Cimento,  5,  34,  1879. 
Kohlrausch-Loomis,  Pogg.  Ann.  141. 
Pisati,  loc.  cit. 
K  and  L,  loc.  cit. 
Pisati,  loc.  cit. 
K  and  L,  loc.  cit. 
Pisati,  loc.  cit. 

M 

•^* 

.    ,     . 

M 

Platinum   .    . 

.    .    . 

Silver    .    .    . 

Steel 

nt*  =  «w  [i  —  o  (t—  15)]  ;  Horton,  Philos.  Trans 

.204  A,  1905. 

Copper 
Copper  (com- 
mercial) 
Iron 
Steel 

4-37* 

3.80 
8.26 
8-45 

a  =.00039 

.00038 
.00029 
.00026 

Platinum 
Gold 
Silver 
Aluminum 

6.46* 
2-55 

a  =  .00012 
.00031 
.00048 
.00148 

Tin  i. 
Lead  o. 
Cadmium  2. 
Quartz  3. 

eo*  o  =  .  00416 
80           .00164 
31           .0058 

DO               .OOOI2 

SMITHSONIAN  TABLES. 


*  Modulus  of  rigidity  in  io11  dynes  per  sq.  cm. 


Young's  Modulus 


TABLE  48. 
ELASTIC  MODULI. 

Young's  Modulus. 

Intensity  of  longitudinal  stress  (kg.  per  sq.  mm.)t 
Elongation  per  unit  length 


75 


Substance. 

<r 

|| 

Ii 

Substance. 

Temp. 

K 

ii 

i    • 

Aluminum       .... 

Lead,  drawn  .... 
"     annealed     .    .    . 
Bronze        ..... 

20 
12.3 
IS 
IS 

IS 
IS 
o 

15.6 

20 

IS 
IS 
12-9 

'5 

15 

0 
20 
19-5 
IS 
0 

20 

ii-S 

7200 
7462 
1803 

1727 
9194 
7070 
11697 
20869 
20794 
20310 
21740 
11713 
15750 
19385 
20500 
8131 

12450 
10520 
12140 
12550 
13220 

8543 
9810 

IO22O 

993° 
10450 
12094 
"550 
13300 
20300 
22790 

i 

2 

3 
3 
4 

1 

3 
3 

8 
4 
9 

i 

10 

3 
3 

2 

3 
3 
7 
i 

9 
3 
7 
ii 
10 
9 
4 
ii 

9 

5 

12 
II 

2 

Nickel-steel,  5^%  ni.    . 
"     .     u      25%  ««      . 
Palladium,  annealed    . 
Phosphor-bronze     .    . 
Platinum,  drawn      .    . 
annealed      . 

IS 

IS 

IS 
13.2 

10 

15 
15 

IS 

IS 

IS 
iS-S 

IS 
IS 

9709 

I2OIO 
17044 
I55I8 
10020 
15989 

7357 
7140 
18810 
17280 
19550 
19560 
21136 

2III2 
21700 
20705 
20910 
2O6OO 
3190 

8734 
4148 
1700 
(  6000 

I  to 

(8000 

i  t0 
(  2500 
6316 

8^85 

13 
13 

3 
ii 

3 
3 

2 
I 

3 
3 
3 
3 
3 
3 
4 
4 
9 
13 
13 
13 
5 
3 
3 
13 

24 
24 
24 

Cadmium    .    .         .    . 

Delta  metal     .... 
Iron,  drawn     .... 
annealed    .    .    . 

"         drawn      .    . 
Silver,  drawn  .... 
"       annealed       .     . 
Steel  wire,  drawn    .    . 
"        "     annealed    . 
Steel,  cast,  drawn    .     . 
"     annealed    . 
Bessemer  .    .    . 
puddle  .... 

cast 

drawn    .... 
"     drawn    .... 
Gold,  drawn    .... 
"     annealed    .    .    . 
"     drawn    .... 
Copper,  drawn    .     .    . 
"       annealed    .    . 
"       drawn    .    .    . 
"       drawn    .    .     . 
"       electr.  h'd  d'n 
Brass,  drawn  .... 

very  soft    .    .     . 
half  soft    .    .    . 
"     hard      .... 
Bismuth      

Zinc,  drawn    .... 
Tin,  drawn     .... 
"    cast    

Glass      .,..,. 

"      drawn  .... 

a 

German  silver     ... 
h'd  d'n 

Nickel    ...... 

Marbles  

Granites     

Basic  intrusives  .     .     . 
Rocks  :   See  Nagaoka, 
Philos.  Mag.  1900. 

"      hard  drawn  .    . 

i  Slotte,  Acta  Soc.  Fenn.  26,  1899;  29,  1900".      10  Baumeister,  Wied.  Ann.  18,  1883. 
2  Meyer,  Wied.  Ann.  59,  1896.                              n  Searle,  Philos.  Mag.  (5)  49,  1900. 
3  Wertheim,  Ann.  chim.  phys.  (3    12,  1844.         12  Cantone,  Wied.  Beibl.  14,  1890. 
4  Pscheidl,  Wien.  Ber.  II,  79,  1879.                     I3  Mercadier,  C.  R.  113,  1891. 
5  Voigt,  Wied.  Ann.  48,  1893.                               J4  Katzenelsohn,  Diss.  Berlin,  1887. 
6  Amagat,  C.  R.  108,  1889.                                    15  Wertheim,  Pogg.  Ann.  78,  1849. 
7  Kohlrausch,  Loomis,  Pogg.  Ann.  141,  1871.     16  Pisati,  Nuovo  Cimento,  5,  34,  1879. 
8  Thomas,  Drude  Ann.  i,  1900.                           References  17-19,  see  Table  47. 
9  Gray,  etc.,  Proc.  Roy.  Soc.  67,  1900. 

Compiled  partly  from  Landolt-Bornstein's  Physikalisch-Chemische  Tabellen. 
SMITHSONIAN  TABLES. 


7  TABLES  49-52. 

COMPRESSIBILITY,  HARDNESS,  CONTRACTION  OF  ELEMENTS. 

TABLE  49.  —  Compressibility  of  the  More  Important  Solid  Elements. 

Arranged  in  order  of  the  increasing  atomic  weights.     The  numbers  give  the  mean  elastic  change 
of  volume  for  one  megabar  (0.987  atm.)  between  100  and  500  megabars,  multiplied  by  io5. 


Lithium                    8.8 

Potassium       31.5 

Selenium          n.8 

Iodine              13. 

Carbon                     0.5 

Calcium             5.5 

Bromine           51.8 

Caesium           61. 

Sodium                    15.4 

Chromium         0.7 

Rubidium        40. 

Platinum            0.21 

Magnesium               2.7 

Manganese        0.7 

Molybdium       0.26 

Gold                   0.47 

Aluminum                1.3 

Iron                   0.40 

Palladium          0.38 

Mercury             3.71 

Silicon                      0.16 

Nickel               0.27 

Silver                 0.84 

Thallium           2.6 

Red  phosphorus      9.0 

Copper              0.54 

Cadmium           i  9 

Lead                   2.2 

Sulphur                   12.5 

Zinc                    1.5 

Tin                     1.6 

Bismuth            2.8 

Chlorine                  95. 

Arsenic             4.3 

Antimony          2.2 

Stull,  Zeitschr.  Phys.  Chem.  61,  1907. 
TABLE  60.— Hardness. 


Agate               7. 

Brass               3-4. 

Iridosmium                7. 

Sulphur             I'S"2-5 

Alabaster         1.7 

Calimine              5. 

Iron                        4-5. 

Stibnite                   2. 

Alum            2-2.5 

Calcite                 3. 

Kaolin                         i. 

Serpentine           3-4. 

Aluminum        2. 
Amber          2-2.5 

Copper          2.5-3. 
Corundum           9. 

Loess  (o°)                  0.3 
Magnetite                   6. 

Silver                2.5-3. 
Steel                    5-8.5 

Andalusite       7.5 

Diamond           io. 

Marble                    3-4. 

Talc                         i. 

Anthracite       2.2 

Dolomite      3-5-4- 

Meerschaum          2-3. 

Tin                           1.5 

Antimony         3.3 
Apatite             5. 

Feldspar             6. 
Flint                    7. 

Mica                           2.8 
Opal                       4-6. 

Topaz                     8. 
Tourmaline             7.3 

Aragonite         3.5 

Fluorite               4. 

Orthoclase                 6. 

Wax  (o°)                 0.2 

Arsenic            3.5 

Galena                2.5 

Palladium                  4.8 

Wood's  metal        3. 

Asbestos           5. 

Garnet                7. 

Phosphorbronze        4. 

Asphalt         1-2. 

Glass            4.5-6.5 

Platinum                     4.3 

Augite              6. 

Gold             2.5-3. 

Plat-iridium               6.5 

Barite               3.3 
Beryl                 7.8 

Graphite       0.5-1. 
Gypsum        1.6-2. 

Pyrite                         6.3 
Quartz                        7. 

Bell-metal         4. 

Hematite            6. 

Rock-salt                   2. 

Bismuth            2.5 

Hornblende        5.5 

Ross'  metal          2.5-3.0 

Boric  acid        3. 

Iridium                6. 

Silver  chloride           1.3 

From  Landolt-Bornstein-Meyerhoffer  Tables  :  Auerbachs,  Winklemann,  Handb.  der  Phys.  1891. 
TABLE  51.— Relative  Hardness  of  the  Elements. 


c 

1  0.0 

Ru 

6-S 

Cu 

3-° 

Au 

2-5 

Sn 

1.8 

Li 

0.6 

B 

9-5 

Mn 

5-0 

Sb 

3-° 

Te 

2-3 

Sr 

1.8 

P 

°-S 

Cr 

9.0 

Pd 

4-8 

Al 

2.9 

Cd 

2.0 

Ca 

'•5 

K 

o-S 

Os 

7.0 

Fe 

4-5 

Ag 

2.7 

S 

2.0 

Ga 

I-S 

Na 

0.4 

Si 

7.0 

Pt 

4-3 

Bi 

2.5 

Se 

2.0 

Pb 

l-S 

Rb 

o-3 

Ir 

6.5 

As 

3-5 

Zn 

2-5 

Mg 

2.0 

In 

1.2 

Cs 

0.2 

Rydberg,  Zeitschr.  Phys.  Chem.  33,  1900. 
TABLE  52.— Ratio,  p,  of  Transverse  Contraction  to  Longitudinal  Extension  under  Tensile  Stress. 

(Poisson's  Ratio.) 


Metal 

Pb 

Au 

Pd 

Pt 

Ag 

Cu 

Al 

Bi 

Sn 

Ni 

Cd 

Fe 

P 

0-45 

0.42 

0-39 

0-39 

0.38 

o-3S 

o-34 

o-33 

0-33 

0.31 

0.30 

0.28 

From  data  from  Physikalisch-Technischen  Reichsanstalt,  1907.  t 

p  for :  marbles,  0.27 ;  granites,  0.24 ;  basic-intrusives,  0.26 ;  glass,  0.23.    Adams-Coker,  1906. 
SMITHSONIAN  TABLES. 


TABLE  53.  77 

"  ELASTICITY  OF  CRYSTALS.* 

The  formulae  were  deduced  from  experiments  made  on  rectangular  prismatic  bars  cut  from  the  crystal.  These  bars 
were  subjected  to  cross  bending  and  twisting  and  the  corresponding  Elastic  Moduli  deduced.  The  symbols 
o  /3  y,  at  /3t  yt  and  03  /32  yz  represent  the  direction  cosines  of  the  length,  the  greater  and  the  less  transverse 
dimensions  of  the  prism  with  reference  to  the  principal  axis  of  the  crystal.  E  is  the  modulus  for  extension  or 
compression,  and  T  is  the  modulus  for  torsional  rigidity.  The  moduli  are  in  grammes  per  square  centimetre. 


Barite. 
Tnio 
^-  =  16.13*  4  i8.5i0*  +  10.427*+  2(38.79/8V  4  I5-2I7V  4-  8.88a202) 

T(->10 

S|r  =  69.52*  +  1  17.660*  +|i  16.467*  +  2(20.16$  V  4  85.2972a2  +  1 
Beryl  (Emerald). 


io10  -  ..      Oj       Oa  of  the  specimen  make  with  the 

-^-  =  15.00—3.675  cos^2  —  17-536  cos2^  cos%       [     principal  axis  of  the  crystal. 


Fluor  spar. 

TCllO 

!£•  =  13.05  -6.26  (*+ 

^  =  58.04  -  50.08  O  V  +  T2-2 

Pyrites. 


=  18.60  -  17.95  (/8V  +  T2*2 

Rock  salt. 

^  =  3348  -  9.66  (a4+j8*  +  74) 

TrtlO 

^  =  1  54-58  -  77.28  (/8V  +  T2-2  +«W 

Sylvine. 

lg-0  =  75.i_48.2(*+0*  +  74) 

Tnio 

IP^-  =  306.0  -  192.8  (  0V  +  72«2  +  aW 

Topaz. 

^  =  4.34i«*  +  3-460/5*  +  3.7717*  +  2  (3-879W  +  2.8567^  +  2. 

T010 

^  =14.88*  +  16.54/8*+  i6.4574430.89/3V440.8972a2443-5i«2/8a 
Quartz. 

TCvlO 

I|P  =  12.734  (i  -72)24  16.693  (I  -T2)?2  4  9-70574-8.46o/37  (&-& 

TOio 

i-  =  19.665  +  9.060732  +  22.9847V  ~  16.920  [(7/3rf  f*7i)  (3««i  ~  flBi)  -  ^272)] 


*  These  formulae  are  taken  from  Voigt's  papers  (Wied.  Ann.  volt.  31,  34,  and  35). 
SMITHSONIAN  TABLES. 


78  TABLE  54. 

ELASTICITY   OF   CRYSTALS. 

Some  particular  values  of  the  Elastic  Moduli  are  here  given.  Under  E  are  given  moduli  for  extension  or  compression 
in  the  directions  indicated  by  the  subscripts  and  explained  in  the  notes,  and  under  T  the  moduli  for  torsional 
rigidities  round  the  axes  similarly  indicated. 


(a)  REGULAR  SYSTEM.* 


Substance. 

E« 

E6 

Ee 

T« 

Authority. 

Fluor  spar      .    ,    » 
Pyrites  

Rock  salt  .... 

«, 

Sylvinc  .    .    .    .    . 

1473  X  io6 
3530  X  io6 
419X106 
403  X  io6 
401  X  io6 

1008  X  io6 
2530  X  io6 
349Xio6 
339  X  106 

2OQ  X  IO 

910  X  io6 
2310  X  io6 
303  X  io6 

345  X  io6 
1075  X  io6 
I29X  io6 

Voigt.t 
(« 

« 

Koch4 
ii 

« 

172  X  IO6 

196  X  io6 

get  V  IO6 

Voigt 

Sodium  chloride      . 
Potash  alum  .     .    . 
Chrome  alum     .     . 
Iron  alum  .... 

405  X  io6 
181  X  io6 
161  X  io6 
186  X  io6 

319  X  io6 
199  X  io6 
177  X  io6 

— 

Koch. 

Beckenkamp.§ 
« 
« 

(6)  RHOMBIC  SYSTEM.|| 


Substance. 

E! 

E2 

E8 

E« 

E6 

E6 

Authority. 

Barite     . 
Topaz     . 

620  X  io6 
2304  X  io6 

540  X  io6 
2890  X  io6 

959X106 
2652  X  io6 

376  X  io6 
2670  X  io6 

702  X  io6 
2893  X  io6 

740  X  io* 
3180  X  io6 

Voigt. 

Substance. 

T12  =  T21 

T13  =  T31 

T23  =  T32 

Authority. 

Barite      ........ 

283  X  io6 
1336X106 

293  X  io6 
1353X106 

121  X  I06 

U04X  io6 

Voigt. 
« 

Topaz 

In  the  MONOCLINIC  SYSTEM,  Coromilas  (Zeit.  fur  Kryst.  vol.  i  )  gives 

G     sum  1  Emax  ~  ^7  X  io6  at  21.9°  to  the  principal  axis. 
I  £^  =  313X106  at  75-4° 

EmM  ==  22I3  X  lo6  m  the  PrmciPal  ax^s- 

Emm  =  1554  X  io6  at  45°  to  the  principal  axis. 


Mica 


In  the  HEXAGONAL  SYSTEM,  Voigt  gives  measurements  on  a  beryl  crystal  (emerald). 
The  subscripts  indicate  inclination  in  degrees  of  the  axis  of  stress  to  the  principal  axis  of 
the  crystal. 

E0=  2165X108,    £45=1796X106,    E90  =  2312X106, 
TO  =  667  X  io6,      Tgo  =  883  X  io6.      The  smallest  cross  dimension  of  the 
prism  experimented  on  (see  Table  82),  was  in  the  principal  axis  for  this  last  case. 


In  the  RHOMBOHEDRIC  SYSTEM,  Voigt  has  measured  quartz.    The  subscripts  have  the 
same  meaning  as  in  the  hexagonal  system. 

Eo  =  1030  X  io6,    E_  45  =  1 305  X  io6,    E+ 45  =  850  X  io6,    Ego  =  7§5  X  io6, 

To  =  508  X  io6,      T90  =  348  X  io6. 
Baumgarten  1"  gives  for  calcspar 

Eo  =  501  X  io6,    E_  45  =  441  X  io6,    E + 45  =  77 2  X  io6,    E9o  =  79°  X  io6. 


*  In  this  system  the  subscript  a  indicates  that  compression  or  extension  takes  place  along  the  crystalline  axis,  and 
distortion  round  the  axis.  The  subscripts  b  and  c  correspond  to  directions  equally  inclined  to  two  and  normal  to  the 
third  and  equally  inclined  to  all  three  axes  respectively. 

t  Voigt,  "Wied.  Ann."  vol.  31,  34-35;  36,  642. 

i  Koch, ''Wied.  Ann."  vol.  18. 

§  Beckenkamp,  "  Zeit.  fur  Kryst."  vol.  io. 

||  The  subscripts  i,  2,  3  indicate  that  the  three  principal  axes  are  the  axes  of  stress ;  4,  5,  6  that  the  axes  of  stress 
are  in  the  three  principal  planes  at  angles  of  45°  to  the  corresponding  axes. 

f  Baumgarten,  "  Pogg.  Ann."  vol.  152. 

SMITHSONIAN  TABLES. 


TABLES  55-57. 
COMPRESSIBILITY  OF  GASES. 


79 


TABLE  56.—  Relative  Volumes  at  Various  Pressures  and  Temperatures,  the  volume  at  0  C  and  at  1  atmo- 
sphere feeing  taken  as  1 000  000. 


Oxygen. 

Air. 

Nitrogen. 

Hydrogen. 

Atm. 

0° 

99°-5 

i99°-5 

0° 

99°.4 

200°.4 

0° 

99°-5 

1990.6 

0° 

99°-3 

200°.  5 

100 

9265 

_ 

_ 

9730 

_ 

_ 

9910 

_ 

_ 

_ 

_ 

_ 

200 

4570 

700O 

9095 

505o 

7360 

9430 

5'95 

7445 

9532 

5690 

7567 

9420 

300 

3208 

4843 

6283 

3<>58 

5*70 

6622 

3786 

53oi 

6715 

4030 

5286 

6520 

400 

2629 

3«30 

4900 

3036 

4170 

5240 

3142 

4265 

5331 

3207 

4147 

5°75 

500 

23I2 

3244 

4100 

2680 

3565 

4422 

2780 

30.S.S 

4515 

2713 

3462 

4210 

600 

2II5 

2867 

3570 

2450 

3180 

3883 

2543 

3258 

3973 

23*7 

3006 

3627 

700 

1979 

26lO 

3202 

2288 

2904 

35°2 

2374 

2980 

3S89 

2149 

2680 

3212 

800 

1879 

2417 

2929 

2168 

2699 

3219 

2240 

2775 

33°° 

1972 

2444 

2900 

900 

1800 

2268 

2718 

2070 

2544 

3000 

2149 

2616 

3<>85 

1832 

2244 

2657 

1000 

1735 

2I5I 

1992 

2415 

2828 

2068 

1720 

2093 

Amagat :  C.  R.  in,  1890 ;  Ann.  chim.  phys.  (6)  29,  1893. 

TABLE  56.  -  Ethylene. 
pv  at  o°  C  and  i  atm.  =  i. 


Atm. 

0° 

10° 

,00 

30° 

40° 

60° 

80° 

100° 

i37°-5 

i98°.s 

46 

_ 

0.562 

0.684 

_ 

_ 

_ 

_ 

_ 

_ 

_ 

48 

— 

0.508 

— 

_ 

_ 

_ 

_ 

_ 

_ 

_ 

5° 

0.176 

O.42O 

0.629 

0.731 

0.814 

0-954 

1.077 

1.192 

1.374 

1.652 

52 

— 

0.240 

0.598 

— 

— 

— 

— 

— 

— 

— 

54 

— 

0.229 

0.561 

— 

— 

— 

— 

— 

— 

— 

56 

— 

O.227 

0.524 

— 

— 

— 

— 

— 

— 

— 

100 

0.310 

0-33  * 

0.360 

0.403 

0.471 

0.668 

0.847 

1.005 

•247 

1.580 

150 

0.441 

0.459 

0.485 

0.5IS 

O-551 

0.649 

0.776 

0.924 

.178 

1.540 

200 

0.565 

0.585 

0.610 

0.638 

0.669 

0-744 

0.838 

0.946 

.174 

1.537 

300 

0.8o6 

0.827 

0.852 

0.878 

0.908 

0.972 

1.048 

1.133 

.310 

1.628 

500 

1.256 

1.280 

1.308 

'•337 

i-367 

1.431 

1.500 

1-578 

.721 

1.985 

1000 

2.289 

2.321 

2-354 

2-387 

2.422 

2-493 

2.566 

2.643 

2.798 

Amagat,  C.  R.  in,  1890;  116,  1893. 
TABLE  67.  —  Ethylene. 


Pressure  in 

Relative  values  of  PV  at  — 

metres  of 

mercury. 

i6°.3 

20°.3 

30°.  r 

4o°.o 

5o°.o 

6o°.o 

70°.o 

79°-9 

89°.9 

I00°.0 

30 

1950 

2055 

2220 

2410 

2580 

2715 

2865 

2970 

3090 

3225 

60 

810 

900 

IIOO 

1535 

1875 

2100 

2310 

2500 

2680 

2860 

90 

1065 

"95 

1325 

1510 

1710 

1930 

2l6o 

2375 

2565 

120 

1325 

1370 

1440 

1540 

1660 

1780 

1950 

2115 

2305 

2470 

*5° 

1590 

1625 

1690 

1785 

1880 

1990 

2I25 

2250 

2390 

2540 

1  80 

1855 

1890 

1945 

2035 

2130 

2225 

2340 

2450 

2565 

2700 

2IO 

2110 

2145 

2200 

2285 

2375 

2470 

2565 

2680 

2790 

2910 

240 

2360 

2395 

2450 

2540 

2625 

2720 

28lO 

2910 

3015 

3125 

270 

26lO 

2640 

27IO 

2790 

2875 

2965 

3060 

3150 

3240 

3345 

300 

2860 

2890 

2960 

3040 

3I25 

3215 

33°0 

3380 

3470 

3560 

320 

3035 

3065 

3^5 

3200 

3285 

3375 

3470 

3545 

3625 

3710 

Amagat,  Ann.  ohim.  phys.  (6)  22,  1881. 


SMITHSONIAN  TABLES. 


8o 


TABLES  58-60. 
COMPRESSIBILITY  OF  GASES. 

TABLE  58.  —  Carbon  Dioxide. 


Relative  values  of  PV  at  — 

Pressure  in 

mercury. 

l8°.2 

35°-i 

400.2 

5Q°.o 

6o°.o 

7o°.o 

8o°.o 

90°.o 

100°  .0 

3° 

liquid 

2360 

2460 

2590 

273° 

2870 

29 

95 

3120 

3225 

50 

— 

1725 

1900 

2145 

2330 

2525 

26 

5s 

2845 

2980 

80 

625 

75° 

825 

I2OO 

1650 

2225 

2440 

2635 

110 

825 

930 

980 

IO9O 

1275 

1550 

1845 

2105 

2325 

140 

1  020 

1120 

1175 

1250 

1360 

1525 

1715 

1950 

2160 

170 

I2IO 

I3IO 

1360 

143° 

1520 

1645 

1780 

1975 

2135 

200 

1405 

1500 

1550 

1615 

1705 

1810 

1930 

2075 

2215 

230 

1590 

1690 

1730 

I800 

1890 

1990 

2090 

22IO 

2340 

260 

1770 

1870 

1920 

1985 

2070 

2166 

2265 

2375 

2490 

290 

1950 

2O6O 

2IOO 

2170 

2260 

2340 

2440 

2550 

2655 

320 

2135 

2240 

2280 

2360 

2440 

2525 

2620 

2725 

2830 

'    Relative  values  of  pv  ;  pv  at  o°  C.  and  i  atm.  =  i. 

0° 

10° 

20° 

30°           40° 

60°           80° 

.000 

137°     198°      258° 

50 
100 

150 

0.105 
0.202 
0.295 

0.114 
0.213 

0.680 
0.229 
0.326 

0.775     0-75° 

0.255       0.309 
0.346      0.377 

0.984      1.096 

0.66  1     0.873 
0.485     0.68  1 

1.  206 
1.030 

0.878 

1.380 
1.259   1.582    1.847 

1.159     1.530     1.818 

300 

0-559 

0.578 

0-599 

0.623      0.649 

0.710     0.790 

0.890 

1.108     I-493      1.820 

500 

0.891 

0.913 

0.938 

0.963       0.990 

1.054     1.124 

I.2OI 

1.362     1.678 

IOOO 

1.656 

1.685 

1.716 

1.748       1.780 

1.848     1.921 

1.999 

Amagat,  C.  R.  m,  1890;  Ann   chim.  phys.  (6)  29,  1893  ;  22,  1881. 


TABLE  59.  —  Compressibility  of  Gases. 


Gas. 

p.v.  (\  atm.). 

i     d(p.v.) 
p.v.       dp 
=  a. 

/ 

a 
t  =  O 

Density. 

Density. 
Very  small 
pressure. 

pov0(i  atm.). 

P  =  76<"» 

02 

1.00038 

—  .00076 

11.2° 

—  .00094 

32- 

32. 

H2 
NI 

CO 

0.99974 
I.OOOI5 
1.00026 

+  .00052 
—  .00030 
—  .00052 

10.7 
14.9 
13.8 

+  .00053 

—  .00056 
—  .0008  1 

2.015  (i  6°) 

28.005 
28.OOO 

2.0173 
28.016 
28.003 

CO2 

1.00279 

—  .00558 

15.0 

—  .00668 

44.268 

44.014 

N20 

1.00327 

—  .00654 

II.O 

—  .00747 

44.285 

43.996 

Air 

I.OOO26 

—  .00046 

1  1.4 

— 

— 

— 

NH3 

1.00632 

~ 

" 

Rayleigh,  Zeitschr.  Phys.  Chem.  52,  1905. 

TABLE  60.  -  Compressibility  ol  Air  and  Oxygen  between  18°  and  22°  0. 

Pressures  in  metres  of  mercury,  pv,  relative. 


Air 

* 

pv 

24.07 
26968 

34-90 
26908 

45-24 
26791 

55-30 

26789 

64.00 

26778 

72.16 

26792 

84.22 
26840 

101.47 
27041 

214.54 

;  29585 

3°4-Q4 
32488 

02 

P 
pv 

24.07 
26843 

3//9 

26614 

- 

26185 

64.07 

26050 

72.15 

25858 

84.19 
25745 

101.06 
25639 

214.52 
26536 

303-03 
28756 

Amagat,  C.  R.  1879. 


SMITHSONIAN  TABLES. 


TABLES  61-62. 


8l 


RELATION    BETWEEN    PRESSURE,   TEMPERATURE    AND 
VOLUME  OF  SULPHUR  DIOXIDE  AND  AMMONIA.* 


TABLE  61.— Sulphur  Dioxide. 

Original  volume  looooo  under  one  atmosphere  of  pressure  and  the  temperature  of  the  experi- 
ments as  indicated  at  the  top  of  the  different  columns. 


Pressure  in 
Atmos. 

Corresponding  Volume  for  Ex- 
periments at  Temperature  — 

Volume. 

Pressure  in  Atmospheres  for 
Experiments  at  Temperature  — 

S8°.o 

99°.6 

l83°.2 

58°.o 

99°-6 

i83°.2 

10 

8560 

9440 

_ 

12 

6360 

7800 

- 

lOOOO 

- 

9.60 

- 

!c 

4040 

6420 

- 

9000 

9.60 

10-35 

- 

ID 

18 

_ 

S310 
4405 

_ 

8000 

10.40 

11.85 

- 

20 

— 

4030 

— 

7000 

"•55 

I3-05 

— 

24 

28 
32 

- 

3345 
2780 
2305 

3180 

2640 

6000 
5000 

12.30 
13-15 

14.70 
16.70 

— 

36 

- 

I93S 

2260 

4000 

14.00 

20.15 

- 

40 

c 

- 

1450 

2040 
1640 

1375 

3500 
3000 

14.40 

23.00 
26.40 

29.10 

70 

— 

— 

1130 

2500 

— 

30.15 

33-25 

so 

— 

— 

930 

2000 

- 

35-20 

40-95 

9° 

100 

_ 

_ 

79° 
680 

1500 

- 

39.60 

55-20 

120 

- 

- 

545 

1000 

- 

- 

76.00 

140 
160 

- 

- 

430 
325 

500 

•• 

— 

117.20 

TABLE  62.  — Ammonia. 

Original  volume  100000  under  one  atmosphere  of  pressure  and  the  temperature  of  the  experiments  as 
indicated  at  the  top  of  the  different  columns. 


d 

*8g 

5  a 

|l 

Corresponding  Volume  for  Ex- 
periments at  Temperature  — 

Volume. 

Pressure  in  Atmospheres  for  Experiments 
at  Temperature  — 

46°.6 

99°-6 

,830.6 

3o°.a 

46°.6 

99°.6 

.830.0 

10 

95°0 

_ 

_ 

10000 

8.85 

9.50 

_ 

12.5 

7245 

7635 

- 

9000 

9.60 

10.45 

- 

15 
2O 

25 

iO_0U 

4645 
3560 

4875 
3835 

8000 
7OOO 

10.40 
11.05 

11.50 
13.00 

I2.OO 
13.60 

_ 

30 

- 

2875 

3185 

6000 

11.80 

14-75 

15-55 

- 

35 
40 

45 
50 

- 

2440 
2080 

1795 
I490 

2680 

2345 
2035 

1775 

5OOO 
4000 
3500 

12.00 

16.60 

18.35 
18.30 

18.60 
22.70 
25.40 

19.50 
24.00 
27.20 

55 

— 

1250 

1590 

3000 

— 

— 

29.20 

3i-5o 

60 

- 

975 

145° 

2500 

- 

- 

34-25 

37-35 

70 
80 

~ 

I 

1245 
1125 

2OOO 

- 

- 

41-45 

45-50 

90 

- 

- 

1035 

1500 

— 

- 

49.70 

58.00 

100 

950 

IOOO 

59-65 

93-6o 

*  From  the  experiments  of  Roth,  "  Wied.  Ann."  vol.  xi,  1880. 
SMITHSONIAN  TABLES. 


82 


TABLE  63. 
COMPRESSIBILITY  OF  LIQUIDS, 


If  V\  is  the  volume  under  pressure  p\  atmospheres  at  t°C,  and  V%  is  volume  at  pressure  p%  and  the 
same  temperature,  then  the  compressibility  coefficient  may  be  denned  at  that  temperature  as  * 

B i_ 

~Vi 

In  absolute  units  (referred  to  megadynes)  the  coefficient  is 


1.0137 


Substance. 

<• 

Pressures. 

,.,o. 

Ii 

Substance. 

ft 

Pressures. 

/3.io 

is 

Acetone 

o 
o.oo 

1-500 

82 

i 

Methyl  alcohol 

O 

IOO. 

8.68-37-3 

221 

3 

44 

0.00 

500-1000 

59 

ii 

14                        44 

18.10 

8 

120 

2 

44 

0.00 

99-5 

1000-1500 
8.94-36.5 

47 
276 

ii 

3 

Nitric  acid 
Oils:  Almond 

20.3 

1-32 

338 

55 

II 

8 

Benzole 

5-95 

8 

83 

2 

Olive 

20  c 

_ 

63 

ii 

44 

17.9 

8 

92 

14 

Paraffin 

14.8 

_ 

63 

6 

M 

154 

1-4 

87 

4 

Petroleum 

16.5 

- 

70 

12 

'« 

78.8 

1-4 

126 

Rock 

19.4 

- 

75 

8 

Carbon  bisulphide 

0.00 

1-500 

66 

i 

Rape-seed 

20.3 

- 

66 

44 

44                             14 

o.oo 

500-1000 

53 

44 

Turpentin 

19.7 

- 

79 

" 

II                             II 

0.00 

1000-1500 

43 

41 

Toluene 

10. 

- 

79 

13 

Chloroform 

49.2 

0. 

1000-1500 

51 

IOI 

5 

U 

Xylene 

IOO. 
10. 

*• 

150 
74 

14 
44 

" 

20. 

—    • 

128 

14 

" 

IOO. 

— 

132 

41 

• 

40. 

- 

162 

14 

Paraffins:  C6H14 

23- 

O-I 

J59 

14 

" 

60. 

— 

204 

" 

CyHie 

" 

41 

« 

IOO. 

8-9 

211 

3 

CgHig 

M 

«< 

121 

44 

ii 

IOO. 

J9~34 

206 

44 

C9H20 

14 

IJ-3 

II 

Collodium 
Ethyl  alcohol 

14.8 
28. 

150-200 

i 

6 

7 

Ci2H26 

44 
II 

105 

II 
14 

ii          ii 

28. 

150-400 

81 

44 

Ci4H80 

II 

"3 

44 

44                    II 

65. 

i  50-200 

no 

" 

CifiH34 

" 

75 

41 

14                     II 

65. 

150-400 

IOO 

44 

Water 

0. 

1-25 

525 

I 

II                     II 

IOO. 

150-200 

168 

M 

" 

10. 

14 

500 

44 

II                     II 

IOO. 

150-400 

132 

" 

44 

20. 

" 

491 

44 

II                     II 

185. 

i  50-200 

320 

44 

(4 

0. 

25-50 

516 

" 

II                     II 

185. 

150-400 

245 

44 

" 

10. 

492 

II 

II                     II 

310. 

150-200 

4200 

" 

" 

20. 

II 

476 

44 

II                     II 

310. 

150-400 

1530 

44 

41 

0. 

I-IOO 

5" 

41 

II                     II 

0. 

1-50 

96 

I 

" 

10. 

14 

483 

14 

II                     II 

20. 

1-50 

112 

44 

II 

20. 

44 

468 

" 

II                     II 

40. 

1-50 

I25 

II 

II 

50. 

14 

449 

II 

II                     II 

0. 

100-200 

85 

II 

** 

IOO. 

44 

478 

tl 

II                     II 

0. 

300-400 

41 

" 

0. 

100-200 

492 

" 

II                     41 

20. 

300-400 

7^ 

44 

II 

10. 

" 

461 

44 

II                     II 

40. 

300-400 

87 

44 

" 

20. 

44 

442 

44 

II                     II 

0. 

5OO-6OO 

<* 

" 

50. 

41 

425 

44 

II                     It 
II                     l( 

0. 
20. 

700-800 
700-800 

e 

|« 

44 

IOO. 
0. 

1-500 

468 
475 

44 

II                   14 

40. 

700-800 

65 

II 

14 

20.4 

44 

434 

44 

II                   II 

0. 

900-1000 

52 

'« 

« 

48.85 

" 

416 

44 

Ethyl  chloride 

II. 

8.5-34.2 

138 

3 

II 

0. 

5OO-IOOO 

416 

II 

I!          « 

15.2 
61.5 

8.7-37.2 
12.6-34.4 

III 

K 

II 

0. 

20.4 

IOOO-I5OO 
II 

358 
338 

<l 

14  , 

14                    41 

99.0 

12.8-34.5 

495 

* 

" 

48.85 

II 

325 

44 

Glycerine 

14.8 

: 

25 

22 

8 
6 

II 

0. 

o. 

I  500-2000 
2OOO-25OO 

324 
292 

44 

Mercury 
ii 

0. 
0. 

— 

3-92 
3-90 

9 

10 

41 
II 

0. 

48.85 

25OO-3OOO 

261 
254 

44 
44 

Methyl  alcohol 

14.7 

8.50-37.1 

104 

3 

For  references  see  page  83. 


SMITHSONIAN  TABLES. 


TABLE  64. 
COMPRESSIBILITY  AND  BULK  MODULI  OF  SOLIDS. 


Solid. 

Compression 
per  unit 
volume  per 
atmo.  X  io6. 

Authority. 

Calculated  values  of  bulk 
modulus  in  — 

Grammes  per 
sq.  cm. 

Pounds  per 
sq.  in. 

Crystals  :  Barite  

i-93 

0.747 

J.20 
I.I4 

2.67 
4-2O* 

745* 
0.61 
0.113 
0.95 

O.86 
I.  O2 
2.76 

0.68 
2.2-2.9 

Voigt    .    .    . 

<« 

« 

« 

Amagat    .     . 
Buchanan 
Amagat    .     . 

H 
« 
ft 

535  X  io6 

13*4     ' 

906     « 

387      " 
246     " 
138     " 
1694     " 
9140     " 
1090     " 
1202      " 
1012      " 

374    " 
1518    " 

405    " 

7.61  Xio« 

19.68     « 
12.24      " 
12.89     " 
5.50     « 

3-50 
1.97      « 
24.11      ' 
130.10     " 
1548     " 
17.10     " 
1441      " 
5-32      " 
2I.6I      " 
5.76     « 

Beryl   

Fluorspar     

Quartz      

Rock  salt      

Topaz  ...         ... 

Delta  metal          

Lead  

Steel  

Glass  

NOTE:  Winklemann,  Schott,  and  Straulel  (Wied  Ann  61,  63,  1897;  68,  1899)  give  the  following  coefficients  (among 
others)  for  various  Jena  glasses  in  terms  of  the  volume  decrease  divided  by  the  increase  of  pressure  expressed  in  kilo- 
grammes per  square  millimetre : 


No. 

Glass. 

Compres- 
sibility 

No. 

Glass. 

Compres- 
sibility. 

66  e 

7660 

Barytborosilicat             .     .    • 

8208 

Heaviest  Bleisilicat        »    •    •    • 

1299 
IO 

Natronkalkzinksilicat  .... 

2?8 

S  196 

*  Rontgen  and  Schneider  by  piezometric  experiments  obtained  5.0  X  io~«  for  rock  salt,  and  5.6  X  io~+  for  sylvii 
(Wied.  Ann.,  vol.  31). 


References  to  Tables  63  and  64. 


Liquids  (Table  63) : 

1  Amagat,  Ann.  chim.  phys.  (6)  29,  1893. 

2  Rontgen,  Wied.  Ann.  44,  1891. 

3  Amagat,  C.  R.  68,  1869;  (5)  28,  1883. 

4  Pagliani-Palazzo,  Mem.  Acad.  Lin.  (3)  19, 

1883. 

5  Grimaldi,  Zeitschr.  Phys.  Chem.  I,  1887. 

6  de  Metz,  Wied.  Ann.  41.  1890 ;  47,  1892. 


7  Barus,  Sill.  Journ.  39,  1890;  41, 1891;  Bull. 

U.  S.  Geol.  Surv.  1892. 

8  Quincke,  Wied.  Ann.  19, 1893. 

9  Amagat,  Ann.  chim.  phys.  (6)  22,  1891. 

10  Aime,  Ann.  chim.  phys.  (3)  8,  1843. 

11  Colladon-Sturm,  Pogg.  Ann.  12,  1828. 

12  Martini. 

13  de  Keen,  Bull.  Acad.  Roy.  Belg.  (3)  9, 1895. 

14  Batelli,  Phys.  Zeitschr.  28,  29,  1896. 


Solids  (Table  64) : 

Amagat,  C.  R.  108,  1889 ;  J.  de  Phys.  (2)  8, 

1880. 


Buchanan,  Proc.  Roy.  Soc.  Edinb.  io,  1880. 
Voigt,  Wied.  Ann.  31,  1887;  34,  1888;    36, 
1888. 


SMITHSONIAN  TABLES. 


84  TABLE  65. 

SPECIFIC  GRAVITIES  CORRESPONDING  TO  THE  BEAUME  SCALE. 

The  specific  gravities  are  for  I5.56°C  (6o°F)  referred  to  water  at  the  same  temperature  as  unity. 
For  specific  gravities  less  than  unity  the  values  are  calculated  from  the  formula : 

Degrees  Beaume  =  145  —  -^ '4~, — . 

Specific  Gravity 

For  specific  gravities  greater  than  unity  from : 

Degrees  Beaume  =  5 ...  4_ : 130. 

Specific  Gravity       J 


Specific  Gravities  less  than  i. 

0.00 

o.oz 

0.02 

0.03 

0.04 

0.05 

0.06 

O.OJ 

0.08 

0.09 

Specific 

Gravity. 

Degrees  Beaum£ 

O.60 

103.33 

99-51 

95.81 

92.22 

88.75 

85-38 

82.12 

78.95 

75.88 

72.90 

.70 

70.00 

67.18 

64.44 

61.78 

59-19 

56.67 

54-21 

51.82 

49-49 

47.22 

.80 

45-00 

42.84 

40-73 

38.68 

36.67 

34-71 

32.79 

30.92 

29.09 

27.30 

.90 

23-85 

22.17 

20.54 

18.94 

.17-37 

I5-83 

14.33 

12.86 

11.41 

1.  00 

10.00 

Specific  Gravities  greater  than  i. 

O.oo 

O.OI 

O.02 

0.03 

0.04 

0.05 

0.06 

0.07 

0.08 

0.09 

Specific 

Gravity. 

Degrees  Beaume". 

1.  00 

0.00 

1.44 

2.84 

4.22 

5.58 

-    6.91 

8.21 

949 

10.74 

11.97 

I.IO 

1.  20 

1.30 
1.40 

13.18 
24.17 
33-46 
4143 
48.33 
54.38 
5971 
64.44 

14.37 

25.16 

34.31 

42.16 

48.97 
54.94 

60.20 
64.89 

15-54 
26.15 

35-15 
42.89 
49.60 

55-49 
60.70 

65.33 

16.68 
27.11 
35-98 
43-6o 
50-23 
56.04 
61.18 
65.76 

17.81 
28.06 
36.79 
44.31 
50.84 

i  6&20 

18.91 
29.00 
37-59 
45-0° 
SMS 
57-12 
62.14 
66.62 

20.00 

29.92 

38.38 

45-68 
52-05 

21.07 

30-83 
39.16 
46.36 
52.64 

63.08 

22.12 
31.72 

39-93 
47-03 
53-23 
58.69 

23-15 
32.60 
40.68 
47.68 
53-8o 
59.20 

63-99 

SMITHSONIAN  TABLES. 


TABLE  66.  85 

DENSITY  OR  MASS  IN  GRAMMES  PER  CUBIC  CENTIMETRE  AND  POUNDS 
PER  CUBIC  FOOT  OF  THE   ELEMENTS,  LIQUID  OR  SOLID. 


Element. 

Physical  State. 

Grammes  per 
cu.  cm. 

Pounds  per 
cu.  foot. 

Tempera- 
ture.* 

Authority. 

Aluminum 

cast 

2.56-2.58 

160-161 

" 

wrought 

2.65-2.80 

165-175 

" 

pure 

2.58 

161 

4 

Mallet,  1882. 

Antimony 

vacuo-distilled 

6.618 

413.2 

2O 

Kahlbaum,  1902. 

" 

ditto-compressed 

6.691 

20 

" 

Argon 

amorphous 
liquid 

6.22 

1.3845 

386.43 

-I83 

Herard. 
Baly-Donnan. 

" 

• 

1.4233 

88.86 

—189 

ii          it 

Arsenic 

crystallized 

5-73 

358 

14 

" 

amorph.  br.-black 

3.70 

231 

Geuther 

" 

yellow 

3-88 

242 

Linck 

Barium 
Beryllium 
Bismuth 

solid 

3-75 
I.73-2.I3 
9.70-9.90 

108-133 
605-618 

" 

electrolytic 
vacuo-distilled 

9.747 
9.781 

608.5 
610.6 

20 

Classen,  1890. 
Kahlbaum,  1902. 

" 

liquid 

IO.OO 

624 

271 

Vincentini-Omodei. 

" 

solid 

9.67 

604 

271 

it               ii 

Boron 

crystal 

2.5-2.6 

156-162 

M 

amorph.  pure 

2.45 

J53 

Moissan 

Bromine 

liquid 

3-x5 

197 

Cadmium 

cast 
wrought 

!#** 

5-33-5-35 
54i 

"  . 

vacuo-distilled 

8.648 

539-9 

2O 

Kahlbaum,  1902. 

« 

solid 

8-37 

522 

318 

Vincentini-Omodei. 

* 

liquid 

7-99 

498 

318 

i<                ii 

Caesium 

1.88 

117 

Calcium 

1.52 

95 

Arndt,  Ch.  Ber.  1904. 

Carbon 

diamond 

3.47-3'56 

216-222 

Liversidge. 

" 

graphite 

2.10-2.32 

131—145 

Cerium 

electrolytic 

6.79 

424 

Muthmann-Weiss 

" 

pure 

7.02 

438 

«                           (I 

Chlorine 

liquid 

94.1 

-33-6 

Drugman-Ramsay 

Chromium 

6.52-6.73 

407-420 

" 

pure 

6.92 

432 

20 

Moissan. 

Cobalt 

8.71 

544 

21 

Tilden,  Ch.  C.  1898. 

Columbium 

liquid 

7.1-7.4 

440-460 

Copper 

cast 

8.80-8.95 

549-558 

it 

drawn 

8.93-8.95 

557-558 

" 

wrought 

8.85-8.95 

ii 

ii 

electrolytic 
vacuo-distilled 

8.88-8.95 
8.9326 

554-558 
557-7 

20 

Kahlbaum,  1902. 

" 

ditto-compressed 
liquid 

8.9376 
8.217 

558.0 

20 

ii             ii 
Roberts-Wrightson. 

Erbium 

4-77 

298 

St.  Meyer,  Z.  Ph.  Ch.  37. 

Fluorine 

liquid 

1.14 

71 

—  200 

Moissan-Dewar. 

Gallium 

5-93 

370 

23 

de  Boisbaudran. 

Germanium 

341 

2O 

Wimkler. 

Glucinium 

1.86-2.06 

116-127 

Gold 

cast 

T9-3 

1200 

«« 

wrought 

1207 

" 

vacuo-distilled 

18.88 

1178 

20 

Kahlbaum.  1902. 

" 

ditto-compressed 

19.27 

I2O2 

2O 

it, 

Hydrogen 

liquid 

0.070 

4-3 

—252 

Dewar,  Ch.  News,  1904. 

Indium 

7.12-7.42 

444-463 

*  Where  the  temperature  is  not  given,  ordinary  atmospheric  temperature  is  understood. 

Compiled  from  Clarke's  Constants  of  Nature,  Landolt-Bornstein-Meyerhoffer's  Tables,  and  other  sources.    Where 
no  authority  is  stated,  the  values  are  mostly  means  from  various  sources. 

SMITHSONIAN  TABLES. 


86 


TABLE  66  (continued). 


DENSITY  OR  MASS  IN  GRAMMES  PER  CUBIC  CENTIMETRE  AND  POUNDS 
PER  CUBIC  FOOT  OF  THE   ELEMENTS,  LIQUID  OR  SOLID. 


Element. 

Physical  State. 

Grammes  per 
cu.  cm. 

Pounds  per 
cu.  foot. 

Temper- 
ature.* 

Authority. 

Iridium 

22.42 

1399 

17 

Deville-Debray 

Iodine 

4.7-4.9 

293-306 

17 

Iron 

pure 

7.85-7.88 

490-492 

gray  cast 

7-03-7.I3 

439-445 

white  cast 

7.58-7.73 

473-482 

wrought 

7.80-7.90 

487-492 

liquid 

6.88 

429 

Roberts-Austen 

steel 

7.60-7.80 

474-487 

Lanthanum 

6.15 

384 

Muthmann-Weiss 

Lead 

cast 

"•37 

710 

24 

Reich 

wrought 

11.36 

709 

24 

" 

solid 

11.005 

686 

325 

Vincentini-Omodei 

liquid 

10.645 

664 

325 

U                              H 

vacuo-distilled 

11.342 

708.1 

2O 

Kahlbaum,  1902 

Lithium 

ditto-compressed 

n-347 
0-534 

708.4 
33-3 

20 
20 

Richards-Brink,  '07 

Magnesium 

1.69-1.75 

105-109 

Manganese 

7-4 

460 

Mercury 

liquid 

I3-596 

848.8 

O 

Regnault,  Volkmann 

«« 

" 

13.546 

845.7 

2O 

« 

M 

13.690 

854.7 

—38.8 

Vincentini-Omodei 

M 

solid 

14.193 

886.1 

—  38.8 

Mallet 

M 

Molybdenum 
Nickel 

M 

14.383 
8.4-8.6 
8.60-8.90 

897.9 
520-540 
540-550 

-188 

Dewar,  1902 

Niobium 

7.2 

450 

Nitrogen 

liquid 

0.810 

50-5 

—195 

Baly-Donnan,  1902 

" 

44 

0.854 

53-3 

-205 

«           «          << 

Osmium 

22.5 

1400 

Oxygen 
Palladium 

liquid 

11.4 

711 

184 

Phosphorus 

white 

1.83 

114 

" 

red 

2.20 

I37 

« 

metallic 

2-34 

146 

15 

Hittorf 

Platinum 

2I.2-2I-7 

1320-1350 

Potassium 

0.86-0.88 

54-55 

« 

solid 

0.851 

53-7 

62.1 

Vincentini-Omodei 

« 

liquid 

0.830 

53-8 

62.1 

«             « 

Praesodymium 

6-475 

404 

Muthmann-Weiss 

Rhodium 

II.O-I2.I 

686-755 
* 

Rubidium 

1-532 

9  S-O 

20 

Richards-Brink,  '07 

Ruthenium 

12-3 

768 

Samarium 

77-7.8 

480-490 

Muthmann-Weiss 

Selenium 

4.3-4.8 

270-300 

Silicon 

2.O-2.4 

120-150 

Silver 

cast 
wrought 

10.42-10.53 

10.6 

6^57 

vacuo-distilled 

10.492 

655-0 

20 

Kahlbaum,  1902 

ditto-compressed 

10.503 

2O 

liquid 

9-51 

593 

Roberts-Austen 

Sodium 

0.9712 

60.63 

20 

Richards-Brink,  '07 

solid 

0.9519 

59-4 

97-6 

Vincentini-Omodei 

liquid 

0.9287 

58.0 

**  .. 

1.0066 

62.84 

—  188 

Dewar 

Strontium 

2.50-2.58 

156-161 

Matthiessen 

Sulphur 

2.0-2.1 

120-130 

It 

liquid 

I.8I1 

113.1 

"3 

Vincentini-Omodei 

*  Where  the  temperature  is  not  given,  ordinary  atmospheric  temperature  is  understood. 
SMITHSONIAN  TABLES. 


TABLES  66  (f<mtinu,d)  AND  67.    MASS  OF  VARIOUS  SUBSTANCES. 


TABLE  66  (continwd).  —Density  or  Mass  in  grammes  per  cubic  centimetre  and  pounds  per  cubic  foot  of  the 

elements,  liquid  or  solid. 


Element. 

Physical  State. 

Grammes  per 
Ctu  cm. 

Pounds  per 
cu.  foot 

Tempera- 
ture.* 

Authority. 

Tantalum 

10.4-12.8 

650-800 

Tellurium 

crystallized 
amorphous 

6.25 

6.02 

390 
376 

20 

Beljankin. 

Thallium 

11.8-11.9 

736-742 

Thorium 

II.O 

690 

17 

Nilson. 

Tin 

white,  cast 

7.29 

455 

Matthiessen. 

« 

"      wrought 

7-30 

455 

« 

"      crystallized 
"      solid 

6.97-7.18 

7.184 

435-448 
454 

226 

Vincentini-OmodeL 

* 

"      liquid 

6.99 

436 

" 

gray 

5-8 

360 

Titanium 

3-5 

220 

Tungsten 

18.6-19.1 

Il6o-II9O 

Uranium 

18.7    ' 

II7O 

'3 

Zimmermann. 

Vanadium 

5-5 

340 

Roscoe. 

Xenon 

liquid 

220 

Ramsay-Travers. 

Yttrium 

3-8 

240 

St.  Meyer. 

Zinc 

cast 

7.04-7.16 

439-447 

" 

wrought 

7.19 

449 

" 

vacuo-distilled 

6.92 

432 

20 

Kahlbaum,  1902. 

" 

ditto-compressed 

7-13 

445 

2O 

«              « 

M 

liquid 

6.48 

404 

Roberts-Wrightson. 

Zirconium 

4.14 

258 

Froost. 

TABLE  67  —  Mass  in  grammes  per  cubic  centimetre  and  in  pounds  per  oublo  foot  of  different  kinds  of  wood. 

The  wood  is  supposed  to  be  seasoned  and  of  average  dryness. 


Wood. 

Grammes 
per  cubic 
centimetre. 

Pounds 
aer  cubic 
foot. 

Wood. 

Grammes 
per  cubic 
centimetre. 

Pounds 
per  cubic 
foot. 

Alder 

0.42-0.68 

26-42 

Hazel 

0.6b-0.8o 

37-49 

Apple 

0.66-0.84 

41-52 

Hickory 

0.60-0.93 

37-58 

Ash 
Bamboo 
Basswood.    See  Linden. 

0.65-0.85 
0.31-0.40 

40-53 
19-25 

Holly 
Iron-bark 
Juniper 

0.76 
1.03 
0.56 

8 

35 

Beech 

0.70-0.90 

43-56 

Laburnum 

0.92 

57 

Blue  gum 

1.  00 

52 

Lancewood 

0.68-1  .00 

42-62 

Birch 

0.51-0.77 

32-48 

Lignum  vitse 

I-I7-I-33 

73-«3 

Box 
Bullet-tree 

0.95-1.16 
1.05 

59-72 
65 

Linden  or  Lime-tree 
Locust 

0.32-0.59 
0.67-0.71 

20-37 
42-44 

Butternut 

0.38 

24 

Logwood 

.91 

57 

Cedar 

0.49-0.57 

30-35 

Mahogany,  Honduras 

0.66 

35 

Cherry 

0.70-0.90 

43-56 

Spanish 

0.85 

53 

Cork 

O.22-O.26 

14-16 

Maple 

0.62-0.75 

39-47 

Dogwood 
Ebony 

0.76 
I.I  I-I-33 

47 
69-83 

Oak 
Pear-tree 

0.60-0.90 
0.61-0.73 

37-56 
38-45 

Elm 

0.54-0.60 

34-37 

Plum-tree 

0.66-0.78 

41-49 

Fir  or  Pine,  American 

Poplar 

0-35-o-S 

22-31 

White 

0.35-0-  5° 

22-31 

Satinwood 

0-95 

59 

"          Larch 
"          Pitch 
a          Red 

0.50-0.56 
0.83-0.85 
0.48-0.70 

31-35 
52-53 
30-44 

Sycamore 
Teak,  Indian 
"     African 

0.40-0.60 
0.66-0.88 
0.98 

24-37 

r55 

«         Scotch 

0.43-0.53 

27-33 

Walnut 

0.64-0.70 

40-43 

0          Spruce 
"          Yellow 

0.48-0.70 
0.37-0.60 

30-44 
23-37 

Water  gum 
Willow 

I.OO 

0.40-0.60 

24-37 

Greenheart 

0.93-1.04 

58-65 

*  Where  the  temperature  is  not  given,  ordinary  atmospheric  temperature  is  understood. 
SMITHSONIAN  TABLES. 


88  TABLE  68. 

DENSITY  OR  MASS  IN  GRAMMES  PER  CUBIC  CENTIMETRE  AND  POUNDS 
PER  CUBIC  FOOT  OF  VARIOUS  SOLIDS.* 


Substance. 

Grammes 
per  cubic 
centimetre. 

Pounds 
per  cubic 
foot. 

Substance. 

Grammes 
per  cubic 
centimetre. 

Pounds 
per  cubic 
foot. 

Agate 
Alabaster  : 

2.5-2.7 

156-168 

Garnet 
Gas  carbon 

3;<g3-8 

230-335 
119 

Carbonate      .        . 

2.69-2.78 

168-173 

Glass: 

Sulphate 

2.26-2.32 

141-145 

Common 

2.4-2.8 

150-175 

Alum,  potash    . 
Amber 

I.OO-I.II 

109 
66-69 

Flint 
Glauber's  salt    . 

2.9-5.9 
1.4-1.5 

180-370 
87-93 

Anth.r3.citc 

1.4-1.8 

87-112 

Glue   .... 

80 

Apatite      . 

3.16-3.22 

197-201 

Gneiss 

2.4-3.2 

150-200 

Aragonite  .        . 

3-° 

I87 

Granite 

2.0-3.0 

125-187 

.Arsenic 

7c6—K8 

I  O"-2  1 

I2O—I4O 

Asbestos    . 

2.0-2.8 

jy^^oy-3 
125-175 

Gravel 

1.  2-1.8 

94-112 

Asphaltum 
Barite 

1.1-1.5 

4.5 

69-94 
281 

Gray  copper  ore 
Green  stone 

4.4-5.4 
2.9-3.0 

275-335 
180-185 

Basalt 

2.4-3.1 

150-193 

Gum  arabic 

1.3-1.4 

80-85 

Beeswax    . 

0.96-0.97 

60—  6  1 

Gunpowder  : 

Bole  .... 

2.2-2.5 

137-156 

Loose 

0.9 

56 

Bone  .... 

106-125 

Tamped  . 

109 

Boracite    .        .        . 

2.9-3.0 

181-187 

Gypsum,  burnt  . 

1.8? 

.7 

"3 

Borax         .        . 

1.7-1.8 

106-112 

Hornblende 

3-o 

187 

Borax  glass 

2.6 

162 

Ice      .... 

0.88-0.91 

55-57 

Boron        .        . 

2.45-2.69 

153-168 

Iodine 

4-67 

291 

Brick 

1.4-2.2 

87-137 

Ivory  .... 

1.83-1.92 

i  14-120 

Butter 

0.86-0.87 

53-54 

Kaolin 

2.2 

137 

255-280 

Lava: 

Calcspar    . 

2.6-2.8 

162-175 

Basaltic  . 

2.8-3.0 

175-184 

Carbon. 

Trachytic 

2.0-2.7 

125-168 

See  Graphite,  etc. 

Lead  acetate 

2.4 

150 

Caoutchouc 

0.92-0.99 

57-62 

Leather  : 

Celestine   . 

3-9 

243 

Dry 

0.86 

54 

Cement  : 

Greased  . 

1.02 

64 

Pulverized  loose     . 

1.15-1.7 

72-105 

Lime  : 

Pressed  . 
Set         ... 

1.85 
2.7-3.0 

^68-187 

Mortar    . 
Slaked    . 

1.65-1.78 
I.3-I.4 

103-111 

81-87 

Cetin 

0.88-0.94 

55-59 

Lime  .... 

2.3-3-2 

144-200 

Chalk 

1.9-2.8 

118-175 

Limestone  . 

2.0-3.1 

125-190 

Charcoal  : 

Litharge  : 

Oak 
Pine 

0-57 
0.28-0.44 

35 
1  7-  5-27-5 

Artificial 
Natural   . 

7-8-8.0 

580-585 
489-492 

Chrome  yellow  . 

6.00 

374 

Magnesia    . 

3-2 

200 

Cinnabar   . 

8.12 

507 

Magnesite  . 

3-° 

187 

Clay  .        . 

1.8-2.6 

122-162 

Magnetite  . 

4.9-5.2 

306-324 

Clayslate  . 

2.8-2.9 

175-180 

Malachite   . 

3-7-4-1 

231-256 

Coal,  soft  . 

1.2-1.5 

75-94 

Manganese  : 

Cobaltite    . 

6.4-7.3 

400-455 

Red  ore  . 

346 

216 

Cocoa  butter     . 
Coke 

0.89-0.91 
1.0-1.7 

56-57 
62-105 

Black  ore 
Marble        .        .        . 

3-9-4-I 

2.5-2.8 

243-256 
157-177 

Copal 

1.04-1.14 

65-71 

Marl    .... 

1.6-2.5 

100-156 

Corundum 

3.9-4.0 

245-250 

Masonry 

1.85-2.3 

116-144 

Diamond   . 
Anthracitic    .        . 

3:£3-6 

220-225 
104 

Meerschaum 
Melaphyre  . 

.99-1.28 

2.6 

61.8-79.9 
162 

Carbonado     . 

3.01-3.2  c 

188-203 

Mica   .... 

?  6-3.2 

165-200 

Diorite 

2.8-3  i 

WJ 

I75~I93 

Mortar 

1.75 

109 

Dolomite  . 

2.4-2.9 

150-181 

Mud    .... 

16 

102 

Earth,  dry. 

~J         9 
1.6-1.9 

IOO-I2O 

Nitroglycerine    . 

1.6 

99 

Ebonite 

'•'S 

72 

Ochre 

3-5 

218 

Emery 

4.0 

Opal   .... 

?  2 

J37 

Epsom  salts  : 

Orpiment    . 

34-3-5 

212-218 

Crystalline 

1.7-1.8 

I06-II2 

Paper. 

0.7-1-15 

44-72  ' 

Anhydrous     . 

2.6 

162 

Paraffin 

0.87-0.91 

54-57 

Feldspar    . 

2-53-2.58 

I58-I6I 

Peat    .... 

0.84 

52 

Flint  .... 

*J*J          J 

2.63 

I64 

Phosphorus,  white     . 

1.82 

"4 

Fluor  spar 

196-198 

Pitch  .... 

1.07 

67 

Gabronite  . 

2.9-3.0 

181-187 

Porcelain    . 

2.3-2-5 

Gamboge  . 

1.2 

75 

Porphyry    . 

2.6-2.9 

162-181 

Galena       . 

7-3-7.6 

460-470 

Potash 

2.26 

141      . 

SMITHSONIAN  TABLES. 


For  elements,  see  Table  66. 


TABLES  68  (continued)  AND  69.    DENSITY  OF  VARIOUS  SUBSTANCES.     89 

TABLE  68  (continued).— Density  of  Various  Solids. 


Substance. 

Grammes 
per  cubic 
centimetre. 

Pounds 
per  cubic 
foot. 

Substance. 

Grammes 
per  cubic 
centimetre. 

Pounds 
per  cubic 
foot. 

Pyrites 
Pyrolusite   . 
Pumice  stone 
Quartz 
Resin 
Rock  crystal 
Rock  salt    ; 
Sal  ammoniac 
Saltpetre     . 
Sand: 
Dry.        . 
Damp      . 

4.0-5.2 

3-7-4-6 
0.37-0.9 
2.65 
1.07 

2.6 

2.28-2.41 
1.5-1.6 
1.95-2.08 

1.40-1.65 
1.00-2.0"; 

306-324 
231-287 
23-56 

I5 
67 

162 
142-150 

94-100 
122-130 

87-103 
119-128 

Snow,  loose 
Soapstone,  Steatite     . 
Soda: 
Roasted  . 
Crystalline       .    .     . 
Spathic  iron  ore 
Starch 
Stibnite       . 
Strontianite 
Syenite        . 
Sugar. 
Talc    .... 

0.125 
2.6-2.8 

2-5 

1-45 
3-7-3-9 

4.6-4.7 

3-7 
2.1-3.0 
1.61 

7-8 
162-175 

156 
90 
231-243 
o  c 

287-293 
231 

130-190 

IOO 

1  68 

Sandstone  . 
Selenium     . 
Serpentine  . 
Shale  . 
Silicon 
Siliceous  earth 
Slag,  furnace 
Slate   . 

2.0-3.2 
4.2-4.8 
2.43-2.66 

2.6 

2.O-2.? 

2.66 
2.0-3.9 
2.6-3.3 

124-200 
262-300 
152-166 

I25-i56 
1  66 
124-240 
162-205 

Tallow 
Tellurium   .        .        . 
Tile     .... 
Tinstone 
Topaz 
Tourmaline 
Trachyte     . 
Trap   .... 

0.91-0.97 
6.38-6.42 
1.4-2.3 
6.4-7.0 
3-5-3-6 
2.94-3.24 
2.7-2.8 
2.6-2.7 

570-605 
398-401 
87-M3 
399-437 
219-223 
183-202 
168-175 
162-170 

TABLE  69. —Density  or  Mass  in  Grammes  per  Cubic  Centimetre  and  Pounds  per  Cubic  Foot  of  Various 

Alloys  (Brasses  and  Bronzes). 


Alloy. 

Grammes 
per  cubic 
centimetre. 

Pounds 
per  cubic 
foot. 

8.4.4. 

C27 

"               «                 "             rolled  

8.]6 

£•74, 

"               "                 "             drawn          .        .        . 

870 

C42 

"          Red,  9oCu  +  loZn          
"          White,  5oCu  -f  5oZn       

8.60 
8.  20 

W* 
536 

CH 

8.78 

C4.8 

85Cu  +  i5Sn  
"          8oCu  -j-  2oSn  
«          75Cu  +  25Sn  

8.89 

111 

555 
545 

cci 

German  Silver  :  Chinese,  26-3Cu  +  36.6Zn  +  36.8  Ni 
"            "        Berlin  (i)  52Cu  +  26Zn  -f  22Ni  . 
"            "      (2)  59Cu  4-  3oZn  +  nNi  . 
"      (3)  63Cu  +  3oZn  +  6Ni    . 
Nickelin         
Lead  and  Tin:  87-5Pb  +  i2-5Sn    .... 
"      "      84Pb  +  i6Sn         .... 
"      "      77-8Pb  4-  22.2Sn    

8.30 
8.45 
8-34 
8.30 
8.77 
10.60 

iQ-33 
10.05 

518 
527 

9 

& 

644 
627 

"      "      67.7  Pb  4-  i6.^Sn    . 

0.4-7 

588 

"      "      46vPb4-  ST.  iSn    . 

8.7  -j 

14< 

"      «      3o.5Pb  +  69-5Sn    
Bismuth,  Lead,  and  Tin  :  5361  +  4oPb  -f  7Cd      .... 
Wood's  Metal:  5oBi  +  25Pb  +  i2.5Cd  +  i2.5Sn 
Cadmium  and  Tin  •  32Cd+  68Sn  

t£ 

10.56 
9.70 
7.70 

r4 
659 
605 
480 

Gold  and  Copper  :  9§Au  -f  2Cu     
"         "         o6Au  4-  4Cu 

18.84 
18.36 

^uv 

1176 

114? 

"         "         94Au  4-  6Cu     

I7.qe 

1  1  20 

«         «         92Au  -f-  8Cu     

17.  C2 

IOQ7 

«         «         9oAu  -f-  loCu  

•/  j~ 
I7.I6 

IO7I 

"         "         88Au  -f  i2Cu   
86Au  4-  i4Cu  

1  6.8  1 
16.47 
7.60 

1049 
1027 
480 

"           "         "           nAl  4-  Q<;Cu 

8-37 

tI22 

3Al  +  97Cu         
Aluminum  and  Zinc  :  giA\  -f-  9Zn        
Platinum  and  Iridium  :  9oPt  +  rolr      .        .        .        . 
«           "         «         85Pt  +  iSlr      

8.g 
2.80 
21.62 
21.62 

542 
175 
1348 
H48 

"          "         "         66.67  Pt  4-  7^.77lr 

21.87 

JH" 
1764 

«          "        "          cPt  4-  Qi;Ir 

22.38 

J  7 

I  7Q6 

SMITHSONIAN  TABLES, 


go  TABLE  70. 

DENSITY  OF  LIQUIDS. 

Density  or  mass  in  grammes  per  cubic  centimetre  and  in  pounds  per  cubic  foot  of  various  liquids. 


Liquid. 

Grammes  per 
cubic  centimetre. 

Pounds  per 
cubic  foot 

Temp.  C. 

O.7Q2 

4Q-4 

0° 

O.7QI 

4Q.4 

o 

"         methyl        

O.SlO 

co.e 

o 

O  Ql6 

57-2 

o 

Anilin        

I.O7C 

64.1? 

o 

O.Sqq 

7  -> 

c6.i 

o 

3.187 

IQQ.O 

o 

oxxo-o.g6c. 

•sErr 

W.2-6O.2 

1C 

I.2Q7 

80.6 

1C 

1.480 

Q2.7 

u 

Ether         

0.736 

45.9 

o 

O.66-O.69 

4I.O-47.O 

1.260 

78.6 

o 

Milk  

1.028-1.035 

64.2-64.6 

Naphtha  (wood)        .        .        .        . 

0.848-0.810 
0.665 

52.9-50-5 

41  JK 

0 
1C 

0.800 

4Q.Q 

1C 

0.006 

yry 

61.1 

ii 

O.QIO 

56.8 

^;. 

o  060 

60.  q 

JC 

Cocoanut        ....    \^^  . 

0.925 
0.026 

&t 

^ 

I  O4O-I.IOO 

64.9-68.6 

1C 

Lard        

O.92O 

1:7.4 

1C 

O.877 

54.7 

l( 

Lemon    

0.844 
O.Q42 

52-7 
58.8 

|6 

1C 

OX)OO-O.Q2C 

C6.2-C7.7 

20 

Olive                                 

O  Ql8 

C7.7 

I  e 

Palm       

0.905 

Jl'j 

56.1; 

1C, 

Pine         .        

o  850—0  860 

^^•O—  $4.0 

1C. 

O  Q24. 

1:7.7 

O.QI  C 

C7.I 

1C 

(refined)          

0.913 
o  oce 

57.0 
CQ.6 

15 

I  e 

Train  or  Whale       

O.Qi8—O.Q2i; 

157.^-1:7.7 

1C, 

O.877 

54-2 

16 

Valerian  

0.965 
0.878 

60.2 
•54.8 

16 
o 

"          (light) 

O  7Q  C—  O  80  C. 

40.  6-  SO.  2 

1C 

O.8OO 

4Q.Q 

o 

I.O25 

7"  9 
64.0 

1C 

Soda  lye    

I  2IO 

•jet 

17 

Water       

I  OOO 

t  j-j 
62.4. 

A 

SMITHSONIAN  TABLES. 


TABLE  71.  91 

DENSITY  OF  GASES. 

The  following  table  gives  the  density  of  the  gases  at  o°  C,  76  cm.  pressure,  at  sea-level  and  lati- 
tude 45°  relative  to  air  as  unity  and  under  the  same  conditions ;  also  the  weight  of  one  litre  in 
grammes  and  one  cubic  foot  in  pounds. 


Gas. 

Specific 
Gravity. 

Grammes 
per  litre. 

Pounds 
per  cubic 
foot. 

Reference. 

Air 

1.  000 

1.2928 

.08071 

Rayleigh;  Leduc. 

Acetylene 

0.92 

.07254 

Berthelot,  1860. 

Ammonia 

0.7621 

.04758 

Leduc,  C.  R.  125,  1897. 

Argon 

J-379 

1.782 

.1112 

Ramsey-Travers,  Proc.  R.  Soc.  67,  1900. 

Bromine 

7.1426 

•44  59 

Jahn,  1882. 

Butane 

2.01 

/  *     *T**V' 

2.594 

t'tj^ 
.16194 

Frankland,  Ann.  Ch.  Pharm.  71. 

Carbon  dioxide 

1.5291 

jy~t 
1.9652 

.12269 

Rayleigh,  Proc.  R.  Soc.  62,  1897. 

"       monoxide 

0.9672 

1.2506 

.07807 

«              a        <«           <«       t« 

Chlorine 

2.491 

3.1666 

.19769 

Leduc,  C.  R.  125,  1897. 

-_               i  from 
Coal  gas  <  . 

0.320 

0.414 

.02583 

o        /tO 

0.740 

0-957 

•05973 

Cyanogen 

1.  806 

2.3261 

.14522 

Gay-Lussac. 

Ethane 

1-075 

1.3421 

.08379 

Kolbe,  Ann.  Chem.  Pharm.  65. 

Fluorine 

1.26 

1.697 

.1059 

Moissan,  C.  R.  109. 

Helium 
Hydrofluoric  acid 
Hydrobromic  acid 

1.368 
0.7126 
2.71 

0.1787 
0.894 
3.6163 

.01116 
.05581 
.2258 

Ramsey-Travers,  Proc.  R.  Soc.  67,  1900. 
Thorpe-  Hambley,  J.  Chem.  Soc.  53. 
Lowig,  Gmelin-Kraut,  Org.  Chem. 

Hydrochloric  acid 

1.2692 

1.6283 

.10165 

Leduc,  C.  R.  125,  1897. 

Hydrogen 
Hydrogen  sulphide 

0.0696 
1.1895 

0.09004 

.005621 
.09508 

Rayleigh,  Proc.  R.  Soc.  53,  1893. 
Leduc,  C.  R.  125,  1897. 

Krypton 
Methane 

2.818 
0.5576 

3.654 
0.7160 

.2281 
.04470 

Ramsey-Travers,  Proc.  R.  Soc.  67,  1900. 
Thomson. 

Neon 

0.674 

0.893 

.0558 

Ramsey-Travers,  Proc.  R.  Soc.  67,  1900. 

Nitrogen 
Nitric  oxide,  NO 

0.9673 
1.0387 

1.2542 
I-34I7 

.07829 
.08376 

Rayleigh,  Proc.  R.  Soc.  62,  1897. 
Leduc,  C.  R.  116,  1893. 

Nitrous  oxide,  N2O 

1.9688 

.12291 

»       C.R.  125,  1897. 

Oxygen 
Sulphur  dioxide 

I-°53 
2.2639 

1.4292 
2.8611 

.08922 
.17862 

Rayleigh,  Proc.  R.  Soc.  62,  1897. 
Leduc,  C.  R.  117,  1893. 

Steam  at  100° 

0.469 

0.581 

•0363 

Xenon 

4.422 

5-717 

'3569 

Ramsey-Travers,  Proc.  R.  Soc.  67,  1900. 

Compiled  partly  from  Landolt-Bornstein-Meyerhoffer's  Physikalisch-Chemische  Tabellen. 
SMITHSONIAN  TABLES. 


92  TABLE  72." 

DENSITY  OF   AQUEOUS  SOLUTIONS.* 

The  following  table  gives  the  density  of  solutions  of  various  salts  in  water.     The  numbers  give  the  weight  in 
grammes  per  cubic  centimetre.     For  brevity  the  substance  is  indicated  by  formula  only. 


Substance. 

Weight  of  the  dissolved  substance  in  100  parts  by  weight  of 
the  solution. 

0 

d 

Authority. 

5 

10 

15 

20 

25 

30 

40 

5° 

60 

K2O   .     . 

T  O4.7 

.098 

1.153 

I.2I4 

1.284 

1-354 

I-503 

1.659 

1.809 

i5- 

Schiff. 

KOH      .     .     . 

I.O4O 

.082 

1.027 

I.O76 

1.229 

1.286 

I.4IO 

J'538 

1.666 

" 

Na2O      .    .    . 
NaOH    .    .    . 
NH8  .... 

1.073 
1.058 
0.978 

.144 
.114 
0-959 

1.218 
1.169 

0.940 

1.284 
1.224 
0.924 

1-354 
1.279 
0.909 

1.421 

$6 

1-557 
1.436 

1-539 

1.829 
1.642 

il 

ti 

Carius. 

NH4C1  .     . 

I.OI5 

.030 

1.044 

1.058 

1.072 

- 

_ 

. 

- 

i5. 

Gerlach. 

KC1   .... 

T  O~*  I 

06  c 

I  OQQ 

I  I  ^  C 

— 

_ 

^m 

. 

mm 

j  r 

!• 

NaCl.    .    .    . 

•v-"Jj 
.072 

njyy 
I.  IIO 

1*1  CO 

I.IQI 

: 

I  C. 

(i 

LiCl  .... 
CaCl2     .    .    . 

I.O29 
I.04I 

•  V  /  *• 

1.057 
1.086 

1.085 
I.I32 

i!ii6 
1.181 

*"*  7 
I.I47 
1.232 

I.lSl 
1.286 

-255 
.402 

- 

- 

*  J* 

15- 

" 

CaCl2  +  6H2O 

I.OI9 

1.040 

1.  06  1 

1.083 

I.IO5 

I.I28 

.176 

1.225 

1.276 

18. 

Schiff. 

AlClg      .    .    . 

I.O35 

1.072 

I.  Ill 

I-I53 

I.I96 

I.24I 

•340 

— 

15. 

Gerlach. 

MgCl2    .    .    . 

I.04I 

1.085 

I.I30 

1.177 

1.226 

1.278 

_ 

_ 

15. 

« 

MgCl2+6H2O 
ZnCl2     .    .    . 

I.OI4 
1.043 

1.032 
1.089 

1.049 
LI35 

1.067 
1.184 

1.085 
1.236 

I.IO3 
1.289 

.141 
.417 

1.183 
1-563 

1.222 
L737 

24. 
19-5 

Schiff. 
Kremers. 

CdCl2     .    .    , 

1.043 

1.087 

I.I38 

I-I93 

1.254 

1.319 

1.469 

1-653 

1.887 

19-5 

« 

SrCl2.    .    .    . 

1.044 

1.092 

I-I43 

1.198 

L257 

I.32I 

— 

- 

Gerlach. 

SrCl2  +  6H20 

1.027 

I-°53 

1.082 

i.  in 

1.042 

I.I74 

1.242 

1.317 

- 

15. 

" 

BaCl2     .    .    . 
BaCl2+2H2O 

1.045 
L035 

1.094 
1.075 

I.I47 
I.II9 

1.205 
1.166 

1.269 

1.217 

1-273 

™" 

•• 

"* 

i5- 

21. 

Schiff. 

CuCl2     .    .    . 

1.044 

1.091 

I-I55 

I.22I 

1.291 

1.360 

1.527 

•. 

- 

'7-5 

Franz. 

NC12.    .    .    . 

1.048 

1.098 

LI57 

1.223 

1.299 

— 

_ 

— 

'7-5 

" 

HgCl2    .    .    . 

I.O4I 

1.092 

— 

_ 

_ 

_ 

20. 

Mendelejeff. 

Fe2Cl6    .    .    . 

I.O4I 

i.  086 

I.I30 

I.I79 

1.232 

I.2OX) 

1.413 

T-545 

1.668 

17.5 

Hager. 

PtCl4.    .    .    . 

1.046 

1.097 

I-I53 

I.2I4 

1.285 

1.362 

1.546 

1-785 

- 

— 

Precht. 

SnCl2  +  2H2O 

1.032 

1.067 

I.I04 

I-I43 

1.185 

1.229 

1.329 

1.444 

1.580 

I5. 

Gerlach. 

SnCl4+5H2O 

1.029 

1.058 

1.089 

1.  122 

1.157 

I-I93 

1.274 

L365 

1.467 

15. 

" 

LiBr  .... 

T  O*?3 

I.O7O 

I.  Ill 

I.I  C4 

I.2O2 

I  2  C2 

i  ^66 

i  408 

IOC 

Kremers. 

KBr 

T  O1  C 

J.  *\J  1  W 

1.073 

I.II4 

•••  JT" 

I.2O5 

•»*3* 

1.254 

1  *J  \S\J 

1.364 

i  .^.yo 

_ 

19-5 

M 

NaBr      .    .    . 

1.078 

I.I23 

I.I72 

1.224 

1.279 

1.408 

1-563 

— 

19-5 

" 

MgBr2    .    .    . 

I.04I 

1.085 

I-I35 

I.I89 

1.245 

1.308 

1-449 

1.623 

_ 

19-5 

« 

ZnBr2     .    .    . 

1.043 

1.091 

I.I94 

1.202 

1.263 

1.328 

1-473 

1.648 

1-873 

19-5 

M 

CdBr2     .     .    . 

I.04I 

1.088 

I-I39 

I.I97 

1.258 

1.324 

1.479 

.678 

— 

19.5 

it 

CaBr2     .    .    . 

1.042 

1.087 

I.I92 

2.250 

1-313 

1-459 

•639 

— 

19-5 

U 

BaBr2     .    .     . 

1.043 

1.090 

I.I42 

I.I99 

1.260 

1.327 

1-483 

.683 

— 

19-5 

u 

SrBr2      .    .    . 

1.043 

1.089 

I.I40 

I.I98 

1.260 

1.328 

1.489 

•693 

1-953 

19-5 

a 

KI      .... 

1.076 

1.118 

I.l64 

1.216 

1.260 

k*«*M 

1.  7  '32 

IQ-C 

tt 

Lil     .... 

1.036 

1.077 

1.  122 

T^ 

I.I7O 

1.222 

1.278 

1.412 

•573 

*•'/  j^ 

1-775 

7  J 

*9*5 

« 

Nal    .... 

1.038 

1.080 

1,126 

I.I77 

1.232 

1.292 

1.430 

•598 

i.  808 

I9-5 

" 

ZnI2  .    .    . 

1.043 

1.089 

I.I38 

1.194 

1.253 

1.366 

1.418 

.648 

1-873 

J9-5 

" 

CdI2  .... 

1.  086 

i.n6 

1.  102 

" 

I  2CI 

1.  717 

I  474 

1.678 

_ 

IQ.C 

M 

1.086 
1.088 

a.ijfw 

I-I37 
I.I38 

I.I92 
I.I96 

1.252 
1.258 

*-  j*  i 
1.318 

1.472 
1-475 

1.666 
1.663 

1.913 
1.908 

7  D 

« 

CaI2  .... 

I.O42 

SrI2   .... 

1.043 

1.089 

I.I40 

I.I98 

1.260 

1-328 

1.489 

1.693 

1.953 

i9-5 

" 

BaI2  .... 

1.043 

1.089 

I.I4I 

I.I99 

1.263 

I-33I 

1-493 

1.702 

1.968 

J9-5 

NaClOg.     .    . 
NaBrOg.     .    . 

1-035 
1.039 

1.  068 
1.081 

1.106 
1.127 

1.14-j 
I.I76 

I.I88 
1.229 

1-233 

1.287 

1.329 

- 

- 

19-5 

" 

KNO8     .    .    . 

I.O3I 

1.064 

1.099 

I-I35 

_ 

_ 

_ 

_ 

15. 

Gerlach. 

NaNOg  .     .     . 

I.03I 

1.065 

I.IOI 

1.140 

1.180 

1.222 

I-3I3 

1.416 

_ 

20.2 

Schiff. 

AgNOg  .    .    . 

1.044 

1.090 

1.140 

•'95 

1-255 

1.322 

1.479 

1-675 

1.918 

15- 

Kohlrausch.  . 

*  Compiled  from  two  papers  on  the  subject  by  Gerlach  in  the  "  Zeit.  fur  Anal.  Chim.,"  vols.  8  and  27. 
SMITHSONIAN  TABLES. 


TABLE  72  (continued). 
DENSITY   OF   AQUEOUS  SOLUTIONS, 


93 


Weight  of  the  dissolved  substance  in  100  parts  by  weight  of 

the  solution. 

0 

Substance. 

ti 

Authority. 

5 

10 

15 

20 

*5 

30 

40 

So 

60 

H 

NH4N03     .    .     . 

I.O2O 

I.04I 

1.063 

1.085 

I.I07 

1.131 

1.178 

1.229 

1.282 

17. 

Gerlach. 

ZnNO3    .... 

1.048 

1.095 

1.146 

I.2OI 

1.263 

1.325 

1.456 

I-597 

_ 

17. 

Franz. 

ZnN03+6H2O     . 
Ca(N03)2    .    .    . 

1-037 

1.054 
1-075 

1.118 

I.IIj 
I.I62 

1.  211 

1.178 
1.260 

1.250 
1.367 

1.329 
1.482 

1.604 

14. 
17- 

Oudemans. 
Gerlach. 

Cu(N03)2    .    .    . 

1.044 

1.093 

1.143 

1.203 

1.263 

1.328 

1.471 

- 

- 

17. 

Franz. 

Sr(N03)2     .    .    . 

1.039 

1.083 

1.129 

I.I79 

- 

- 

- 

- 

- 

19. 

Kremers. 

Pb(N03)2    .    .    . 

1.043 

I.09I 

I«I43 

I.I99 

1.262 

I-332 

— 

— 

— 

17. 

Gerlach. 

Cd(NO3)2    .    .    . 

1.052 

1.097 

1.150 

1.  212 

1.283 

'•355 

1-536 

1-759 

- 

17- 

Franz. 

Co(N03)2    .    .    . 

1.045 

I.OOX) 

I.I37 

I.I92 

1.252 

1.318 

1.465 

— 

17- 

it 

Ni(N03)2     .    .    . 

1.045 

1.090 

I-I37 

I.I92 

1.252 

1.318 

1.465 

— 

- 

17- 

u 

I  Fe2(N03)6  .    .    . 
Mg(N03)2+6H20 
Mn(NO8)2+6H2O 

1.039 
I.OlS 
1.025 

1.076 
1.038 
1.052 

1.117 

i.  060 
1.079 

1.160 

1.082 
I.I08 

I.2IO 
I.IOC 
I.I38 

1.261 
1.129 
1.169 

1.373 
1.179 

1.235 

1.496 
1.232 
1.307 

I-657 
1.386 

21 
8 

H 

Schiff. 
Oudemans. 

K2CO3    .... 

1.044 

1.092 

1.141 

I.I92 

1.245 

1.300 

1.417 

'.543 

IS 

Gerlach. 

K2CO3+2H2O  . 

1.037 

I.O72 

I.  IIO 

I.I5O 

I.I9I 

I-233 

1.320 

1.415 

I.5II 

'5- 

" 

Na2CO3ioH2O     . 

I.OI9 

1.038 

L057 

1.077 

1.098 

1.118 

_ 

_ 

_ 

I^. 

u 

(NH4)2S04      .    . 

1.027 

I.O55 

1.084 

I.II3 

I.I42 

1.170 

1.226 

1.287 

_ 

19. 

Schiff. 

Fe2(S04)3    .     .    . 

1.045 
I.O25 

1.096 

I'°53 

1.081 

1.207 
I.  Ill 

1.270 
I.I4I 

I-336 
I.I73 

1.489 
1.238 

— 

: 

18. 
17.2 

Hager. 
Schiff. 

Mgso44  ,7.2.  ; 

I.05I 

1.104 

1.161 

I.22I 

1.284 

- 

- 

- 

IS 

Gerlach. 

MgSO  +  7H2O  . 

1.025 

1.050 

1.075 

I.IOI 

I.I29 

1.155 

1.215 

1.278 

_ 

I5« 

" 

Na2So4  +  ioH2O 
CuS04+5H20   . 

I.OI9 
I.O3I 

1.039 
1.064 

1.059 

I.oSl 
I-I34 

1.  102 
I-I73 

1.124 
1-213 

_ 

— 

It 

u 

Schiff. 

MnSO4-{~4H2O  . 

I.O3I 

1.064 

1.099 

I.I35 

I.I74 

1.214 

'.303 

1.398 

— 

15. 

Gerlach. 

ZnSO4+7H2O    . 

1.027 

L057 

1.089 

1.  122 

I.I56 

1.191 

1.269 

1.443 

20.5 

Schiff. 

Fe2(SO)3+K2S04 

-f-24H2O  .    .    . 

1.026 

1.045 

1.066 

1.088 

1.  112 

1.141 

M 

_ 

_ 

17.5 

Franz. 

Cr2(SO)3+K2S04 

+  24H20     .    . 

1.016 

1-033 

1.051 

1-073 

1.099 

1.126 

1.188 

1.287 

1.454 

17.5 

u 

MgS04  +  K2S04 

-f  6H2O  .    .    . 

1.032 

1.066 

I.IOI 

I.I38 

_ 

_ 

_ 

_ 

_ 

15. 

Schiff. 

(NH4)2S04  + 

FeS04  +  6H20 

.028 

1.058 

1.090 

1.  122 

I.I54 

1.191 

- 

- 

- 

19. 

" 

JCoCrOj. 

1.082 

I  127 

r  T  7  1 

[.225 

I.27Q 

I  ^Q7 

mf 

^  l 

JQ  r 

ti 

K2Cr207      .    .    . 

-035 

1.071 

»•*•/ 

I.I08 

'_ 

*•*/  y 

'_ 

_ 

__ 

*y  j 
19.5 

Kremers. 

Fe(Cy)6K4  .    .    . 

.028 

1.059 

1.092 

1.126 

- 

- 

- 

- 

- 

IS- 

Schiff. 

Fe(Cy)6K3  .     .    . 

.025 

I-°53 

I.I45 

1.179 

— 

— 

— 

— 

— 

13 

it 

Pb(C2H302)2  + 

3H2O  .... 

T  O7I 

1.064 

I.IOO 

1.137 

I.I77 

1.220 

1-315 

1.426 

— 

IS- 

Gerlach. 

2NaOH  +  As2O6 

+  24H20     .    . 

I.O2O 

1.042 

1.066 

1.089 

I.II4 

I.I40 

1.194 

- 

- 

14. 

Schiff. 

5 

10 

<s 

20 

3° 

40 

60 

80 

100 

SO8 

1.084 

I  IT» 

I  I7Q 

I  789 

T  -^ 

1.840 

ir. 

Brineau. 

SOa      , 

I.OI7 

1.028 

I  O4C 

1.067 

_ 

_ 

j 

A 

Schiff. 

*****  j 
O77 

[.069 

[.104 

i.V"-/J 

[.141 

.217 

2QJ. 

1.422 

co6 

T" 

r  r 

Kolb. 

C  H  O 

O2I 

1.047 
1.038 

1.070 
1.058 

1.096 

I.O7Q 

•  ^i  i 
.150 

.207 
.170 

***T 
1.277 

'- 

- 

1  J- 

Gerlach. 

u 

C6H8O7  . 

018 

Cane  sugar  .    .    . 

.019 

1.039 

1.  060 

/  7 
1.082 

.129 

/  W 

.178 

/  o 

1.289 

_ 

_ 

17-5 

« 

HC1    

.021; 

1.050 

1.  07  ft 

I.IOI 

.ICI 

.2OO 

^ 

_ 

i— 

1C.. 

Kolb. 

HBr    

J 

/  J 

.114 

i.icS 

J 

.376 

__ 

_ 

J 

[4. 

Topsoe. 

HI      

T  O77 

1  .07  7 

»j" 
1.161; 

.271 

-J/ 
.4OO 

_ 

^ 

*T 

17. 

H2S04    .... 

1.032 

*  v//  / 
1.069 

Iio6 

l-AW^ 

I.I45 

I 

.223 

.307 

1.501 

1-732 

i.8~38 

•*  J 

Kolb. 

H2SiFl6  .... 

I.O4O 

1.082 

.127 

I.I74 

•273 

- 

- 

_. 

_ 

17.5 

Stolba. 

PoOs    . 

T  O7  C. 

[  O77 

I  IQ 

I.I67 

.271 

—  o  r 

1.676 

I7.c 

fjasrer. 

1.027 

l-W/  / 

1-057 

•  *  *  V 

i.  086 

*••*  V/ 

I.II9 

.188 

;264 

*'W" 

1.438 

_ 

_ 

*  /  j 

*AAKv*« 

Schiff. 

HNO.    .    2.    .'    ] 

T  028 

1.056 

i.  088 

I.  IIO 

.184 

.2  CO 

1.777 

[  A.  CO 

1.528 

1C. 

Kolb. 

C2H402  .... 

I.OO7 

1.014 

i.  02  1 

*  ;/ 
1.028 

AV**T 

1.041 

***  j** 

.052 

3'  x 
1.068 

1.075 

1-055 

j 

IS- 

Oudemans. 

SMITHSONIAN  TABLES. 


94 


TABLE  73. 


DENSITY  OF  WATER  AT  DIFFERENT  TEMPERATURES 
BETWEEN  0°  AND  36°C. 

The  temperatures  are  for  the  hydrogen  thermometer. 


Temp.  C. 

.0 

.1 

.9 

.3 

.4 

.5 

.6 

,7 

.8 

.9 

Q 

0.999  868 

874 

881 

887 

893 

899 

905 

911 

916 

922 

I 

927 

932 

936 

941 

945 

950 

954 

957 

96l 

965 

2 

968 

971 

974 

977 

980 

982 

985 

987 

989 

991 

3 

992 

994 

995 

996 

997 

998 

999 

999 

000 

000 

4 

1.  000  000 

ooo 

ooo 

999* 

999* 

998* 

997* 

996* 

995* 

993* 

5 

0.999992 

990 

988 

986 

984 

982 

979 

977 

974 

971 

6 

968 

965 

962 

958 

954 

95  * 

947 

943 

7 

929 

925 

920 

915 

910 

904 

899 

893 

888 

882 

8 

876 

870 

864 

857 

851 

844 

830 

823 

816 

9 

808 

801 

793 

785 

778 

769 

761 

753 

744 

736 

10 

727 

718 

709 

700 

691 

681 

672 

662 

652 

642 

ii 

632 

622 

612 

601 

580 

569 

558 

547 

536 

12 

525 

5J3 

502 

490 

478 

466 

454 

442 

429 

13 

404 

39  i 

379 

366 

353 

339 

326 

312 

299 

285 

271 

257 

241 

229 

215 

200 

186 

171 

156 

141 

15 

126 

in 

096 

08  1 

065 

050 

034 

018 

002 

986* 

16 
17 

0.998  970 
80  1 

%l 

920 

749 

904 
731 

887 

870 
695 

853 
677 

836 
659 

819 
640 

18 

622 

603 

585 

566 

547 

528 

509 

490 

471 

451 

19 

432 

412 

392 

372 

352 

332 

312 

292 

27I 

251 

20 

230 

210 

189 

168 

147 

126 

105 

083 

062 

040 

21 

019 

997* 

975* 

953* 

93i* 

909* 

887* 

864* 

842* 

819* 

22 

0.997  797 

774 

751 

728 

705 

682 

659 

635 

612 

588 

23 

565 

54  1 

5I7 

493 

469 

445 

421 

396 

372 

347 

24 

323 

298 

273 

248 

223 

198 

173 

H7 

122 

096 

25 

071 

045 

019 

994* 

968* 

941* 

915* 

889* 

863* 

836* 

26 

0.996810 

783 

756 

730 

703 

676 

648 

621 

594 

567 

27 

539 

512 

484 

456 

428 

400 

372 

344 

316 

288 

28 

259 

231 

202 

174 

145 

116 

087 

058 

029 

ooo 

29 

0.995971 

941 

912 

882 

853 

823 

793 

763 

733 

703 

30 

673 

643 

613 

582 

552 

521 

491 

460 

429 

398 

32 

367 
052 

336 
020 

£5* 

273 
956* 

242 
924* 

211 
892* 

179 
859* 

148 

827* 

116 

794* 

084 
762* 

33 
34 

0.994729 
398 

696 
364 

663 
330 

630 
296 

597 
263 

564 
229 

195 

498 
161 

464 
126 

431 
092 

35 

058 

023 

989 

954 

920 

885 

850 

815 

780 

745 

If  we  put  D't  for  the  density  of  water  containing  air  and  Dt  for  the 
density  of  water  free  from  air,  we  get  the  following,  due  to  Marek  : 

t=           0123456789     10 

io'(Dt-D't)=25     27     29     31     32     33     33     34     34     33     32 

t=           11    12    13    14    15    16    17    18    19    20—32 

io7(Dt-D't)=3i      29     27     25     22      19     16     12       8       4  negligible 

From  the  obsenrations  of  Thiesen,  Scheel,  and  Diesselhorst,  Wiss.  Abb.  Phys.-Techn.  Reichs. 

3,  68 ;  1900. 

SMITHSONIAN  TABLES. 


TABLE  74. 


95 


VOLUME  IN  CUBIC  CENTIMETRES  AT  VARIOUS  TEMPERA- 
TURES OF  A  CUBIC  CENTIMETRE  OF  WATER  AT  THE 
TEMPERATURE  OF  MAXIMUM  DENSITY. 

The  water  in  this  case  is  supposed  to  be  free  from  air.    The  temperatures  are 
by  the  hydrogen  thermometer. 


Temp.C. 

.0 

.1 

.3 

.3 

.4 

.5 

.6 

.7 

.8 

.9 

0 

i.  ooo  132 

126 

119 

"3 

107 

101 

095 

089 

084 

079 

I 

073 

069 

064 

059 

055 

OS1 

047 

043 

039 

035 

2 

032 

029 

026 

023 

O2O 

018 

Ol6 

013 

Oil 

009 

3 

008 

006 

005 

004 

003 

002 

001 

001 

000 

000 

4 

000 

000 

000 

001 

001 

002 

003 

004 

005 

007 

5 

008 

010 

012 

014 

016 

018 

02  1 

023 

026 

029 

6 

032 

°35 

039 

042 

046 

050 

054 

058 

062 

066 

7 

071 

075 

080 

085 

090 

096 

101 

107 

112 

118 

8 

124 

130 

137 

143 

149 

156 

163 

170 

177 

184 

9 

192 

199 

207 

215 

223 

231 

239 

247 

256 

264 

10 

273 

282 

291 

300 

309 

319 

328 

338 

348 

358 

ii 

368 

378 

388 

399 

409 

420 

431 

442 

453 

464 

12 
13 

476 

596 

487 
609 

499 
622 

5" 

635 

648 

SJ 

688 

702 

584 
715 

14 

729 

743 

757 

772 

786 

800 

815 

830 

844 

859 

15 

874 

890 

905 

920 

936 

951 

967 

983 

999 

015* 

16 

i.ooi  031 

048 

064 

08  1 

098 

114 

131 

148 

165 

183 

17 

2OO 

218 

235 

253 

271 

289 

307 

325 

343 

18 

380 

399 

436 

455 

474 

493 

551 

19 

571 

610 

630 

650 

671 

691 

711 

732 

752 

20 

773 

794 

815 

836 

857 

878 

899 

921 

942 

964 

21 

985 

007* 

029* 

051* 

073* 

096* 

118* 

140* 

163* 

1  86* 

22 

23 

1.002  205 
441 

231 
465 

254 
489 

277 
513 

300 
538 

324 

562 

347 
586 

370 
6n 

394 
635 

418 
660 

24 

685 

710 

735 

760 

785 

810 

835 

861 

886 

912 

25 

938 

964 

990 

016* 

042* 

068* 

094* 

121* 

147* 

174* 

26 

I.O03  2O1 

227 

254 

281 

308 

336 

363 

39° 

418 

445 

27 

473 

501 

329 

556 

585 

613 

641 

669 

698 

726 

28 

755 

783 

812 

841 

870 

899 

928 

957 

987 

01  6* 

29 

1.004046 

075 

105 

135 

165 

194 

225 

255 

285 

3*5 

30 

31 

346 
655 

376 
686 

407 
717 

437 
749 

468 

781 

499 
812 

844 

876 

592 
908 

623 
940 

32 
33 

972 
1.005  299 

005* 

037* 
365 

070* 
399 

IO2* 
432 

135* 
465 

167* 
499 

200* 

533 

I 

266* 
600 

34 

634 

668 

702 

736 

771 

805 

839 

874 

908 

943 

35 

978 

013* 

047* 

082* 

118* 

153* 

188* 

223* 

259* 

294* 

From  the  observations  of  Thiesen,  Scheel,  and  Diesselhorst,  Wiss.  Abh.  Phys.-Techn.  Reichs. 

3,  68 ;  1900. 

SMITHSONIAN  TABLES. 


96  TABLE  75. 

DENSITY  AND  VOLUME  OF  WATER. 

The  mass  of  one  cubic  centimetre  at  4°  C.  is  taken  as  unity. 


Temp.  C. 

Density. 

Volume. 

Temp.  C. 

Density. 

Volume. 

—10° 

0.99815 

I.OOI86 

+35° 

0.99406 

1.00598 

3 

843 
869 

157 

36 
37 

371 
336 

633 
669 

"I 

892 

108 

38 

299 

706 

—6 

912 

088 

39 

262 

743 

—5 

0.99930 

1.00070 

40 

0.99224 

1.00782 

—4 
—3 

945 
958 

055 
042 

42 

186 

821 
861 

—  2 

970 

031 

43 

107 

901 

—  I 

979 

021 

44 

066 

943 

+0 

I 

0.99987 
993 

I.OOOI3 
007 

45 

46 

0.98982 

1.00985 
1.01028 

2 

997 

003 

47 

940 

072 

3 

999 

001 

48 

896 

116 

4 

I.OOOOO 

I.OOOOO 

49 

852 

162 

5 

0.99999 

I.OOOOI 

50 

0.98807 

1.01207 

6 

997 

003 

51 

762 

254 

7 

993 

007 

52 

715 

301 

8 

988 

012 

53 

669 

349 

9 

981 

019 

54 

621 

398 

10 

0-99973 

1.00027 

55 

0.98573 

1.01448 

ii 

963 

037 

60 

324 

705 

12 

952 

048 

65 

059 

979 

13 

940 

060 

70 

0.97781 

1.02270 

927 

073 

75 

489 

576 

15 

0.99913 

1.00087 

80 

0.97183 

1.02899 

16 

897 

103 

85 

0.96865 

1.03237 

17 

880 

120 

90 

534 

590 

18 

862 

138 

95 

192 

959 

19 

843 

157 

100 

0.95838 

1-04343 

20 

0.99823 

I.OOI77 

110 

0.9510 

1.0515 

21 

802 

198 

120 

•9434 

1.0601 

22 

780 

221 

I30 

•9352 

1.0693 

23 

756 

244 

I4O 

.9264 

1.0794 

24 

732 

268 

150 

•9173 

1.0902 

25 

0.99707 

1.00294 

160 

0.9075 

.1019 

26 

681 

320 

170 

.8973 

•"45 

27 

654 

347 

1  80 

.8866 

.1279 

28 

626 

375 

190 

.8750 

.1429 

29 

597 

405 

200 

.8628 

.1590 

30 

0.99567 

1.00435 

210 

0.850 

.177 

31 

537 

466 

220 

•837 

.195 

32 
33 

505 
473 

497 

230 
240 

.823 
.809 

•215 
1.236 

34 

440 

563 

250 

•794 

1.259 

*"From  —10°  to  o°  the  values  are  due  to  means  from  Pierre,  Weidner,  and  Rosetti ; 
from  o°  to  35°,  to  Thiesen,  Scheel,  and  Diesselhorst ;  31°  to  100°,  to  Thiesen ;  ixo° 
to  250°,  to  means  from  the  works  of  Ramsey,  Young,  Waterston,  and  Him. 

SMITHSONIAN  TABLES. 


TABLE  76. 
DENSITY    OF   MERCURY. 


97 


Density  or  mass  in  grammes  per  cubic  centimetre,  and  the  volume  in  cubic 
centimetres  of  one  gramme  of  mercury.  The  density  at  o°  is  taken  as 
13.59545,*  and  the  volume  at  temperature  /  is  V,=V0(i-}- .000181792* 


Temp.  C. 

Mass  in 
grammes  per 
cu.  cm. 

Volume  of 
i  gramme  in 
cu.  cms. 

Temp.  C. 

Mass  in 
grammes  per 
cu.  cm. 

Volume  of 
i  gramme  in 
cu.  cms. 

—10° 

13.6202 

0.073420^ 

30° 

13-5217 

0.0739552 

—9 

6177 

4338 

31 

5I93 

9686 

—8 

6152 

4472 

32 

5168 

9820 

—7 

6128 

4606 

33 

5J44 

9953 

—6 

6103 

4739 

34 

40087 

—5 

13.6078 

0.0734873 

35 

I3-5095 

0.0740221 

—4 

6053 

5006 

36 

5070 

0354 

—3 

6029 

5140 

5046 

0488 

—  2 

6004 

5273 

38 

5021 

0622 

—  I 

5979 

5407 

39 

4997 

0756 

0 

13-5955 

0.0735540 

40 

13-4973 

0.0740891 

I 

2 

5930 

5674 
5808 

£ 

4729 
4486 

2229 
3569 

3 

5881 

594i 

70 

4244 

4910 

4 

5856 

6075 

80 

4003 

6252 

5 

13-5832 

0.0736209 

90 

13.3762 

0.0747594 

6 

5807 

6342 

100 

3522 

8939 

7 

5782 

6476 

no 

3283 

50285 

8 

5758 

6610 

1  20 

3°44 

1633 

9 

5733 

6744 

130 

2805 

2982 

10 

I3-5708 

0.0736877 

140 

13-2567 

0.0754334 

n 

5684 

7011 

150 

2330 

5688 

12 

5659 
5634 

7M5 
7278 

160 
170 

2093 
1856 

7044 
8402 

14 

5610 

7412 

180 

1620 

9764 

15 

I3-5585 

0-0737546 

190 

13-1384 

0.0761128 

16 

7680 

200 

1148 

2495 

17 

5536 

7813 

2IO 

0913 

3865 

18 
19 

55*2 
5487 

8081 

22O 
230 

0678 
0443 

& 

20 

13.5462 

0.073821? 

240 

13.0209 

0.0767996 

21 

5438 

8348 

250 

12.9975 

9381 

22 

8482 

260 

974i 

70769 

23 

5389 

8616 

270 

95°7 

2161 

24 

5364 

8750 

280 

9273 

,3558 

25 

13.5340 

0.0738883 

290 

12.9039 

0.0774958 

26 

9017 

300 

8806 

6364 

27 

5291 

9i5i 

310 

8572 

7774 

28 

5266 

9285 

320 

8339 

9189 

29 

5242 

9419 

330 

8105 

80609 

30 

13-5217 

0.0739552 

340 

12.7872 

0.0782033 

35° 

7638 

3464 

36° 

7405 

4900 

»  Thiesen  und  Scheel,  Thatigkeitsbericht  der  Phys.  Reichsanstalt,  1897-1898. 
t  Broch,  /.  c. 

SMITHSONIAN  TABLES. 


98  TABLE  77. 

SPECIFIC  GRAVITY  OF   AQUEOUS   ETHYL  ALCOHOL, 


(a)  The  numbers  here  tabulated  are  the  specific  gravities  at  60°  F.,  in  terms  of  water  at  the  same  tempera- 
ture, of  water  containing  the  percentages  by  weight  of  alcohol  of  specific  gravity  .7938,  with  reference  to  the 
same  temperatures.* 

Percentage 
of  alcohol 
by  weight. 

0 

1 

a 

3 

4 

5 

6              7 

8  .           9 

Specific  gravity  at  15°.  56  C.  in  terms  of  water  at  the  same  temperature. 

0 

10 

20 

30 
40 

50 

60 
70 
80 
90 

1.  0000 

.9841 
.9716 
.9578 
.9396 

0.9184 

.8956 

.8721 

.8483 

.8228 

.9981 
.9828 

•9703 
.9560 
•9376 

.9160 
.8932 
.8696 

•8459 
.8199 

•9965 
•9815 
.9691 

•9544 
•9356 

•9135 
.8908 
.8672 

.8434 
.8172 

.9678 
.9528 
•9335 

•9"3 
.8886 
.8649 
.8408 
.8145 

•9930 
•9789 
.9665 

•95" 
•93  i  4 

.9090 
.8863 
.8625 
.8382 
.8118 

.9914 

.9778 
.9652 
.9490 
.9292 

^8603 

•8357 
.8089 

.9898       .9884 
.9766       .9753 
.9638       .9623 
.9470       .9452 
.9270       .9249 

.9047       .9025 
.8816       .8793 
•8581       .8557 
.8331       .8305 
.8061       .8031 

.9869       .9855 
.9741       .9728 
.9609       .9593 
.9434       .9416 
.9228       .9206 

.9001       .8979 
.8769       .8745 
.8533       -8508 
.8279       .8254 
.8001       .7969 

(b)  The  following  are  the  values  adopted  by  the  "  Kaiserlichen  Normal-  Aichungs  Kommission."    They  are 
based  on  Mendelejeff's  formula,t  and  are  for  alcohol  of  specific  gravity  .79425,  at  is3  C.,  in  terms  of  water 
at  15°  C.  ;  temperatures  measured  by  the  hydrogen  thermometer. 

lit 
£-3* 

QJ  ._    *^ 

eu^.n 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Specific  gravity  at  15°  C.  in  terms  of  water  at  the  same  temperature. 

0 

10 

20 

30 
40 

50 

60 

£ 

90 

I.OOOOO 

•98393 
.97164 

•95770 

•93973 

0.91865 
89604 
87265 
84852 
82304 

.99812 
.98262 
.97040 
.95608 
•93773 

.91644 

•89373 
.87028 
.84606 
.82036 

.99630 

•98135 
.96913 

•95443 
•93570 

.91421 
.89141 
.86789 
.84358 
.81763 

•99454 
.98010 
.96783 
•95273 
•93365 

.91197 

.88909 
.86550 
.84108 
.81488 

.99284 
.97888 
.96650 
.95099 
•93157 

.86310 

•83857 
.81207 

.99120 
.97768 

•96513 
.94920 
.92947 

.90746 

•88443 
.86070 
.83604 
.80923 

.98963 
.97648 
•96373 
•94738 
•92734 

.90519 
.88208 
.85828 

•83349 
.80634 

.98812 
.97528 
.96228 

•94552 
.92519 

.90292 

•87974 
.85586 
.83091 
•80339 

.98667 
.97408 
.96080 

•94363 
.92303 

.90063 
.87738 
•85342 
.82832 
.80040 

.98528 
.97287 

.95927 
.94169 
.92085 

.89834 
.87502 
.85098 
.82569 
•79735 

(0)  The  following  values  have  the  same  authority  as  the  last  ;  the  percentage  of  alcohol  being  given  by  volume 
instead  of  by  weight,  and  the  temperature  15°.  56  C.  on  the  mercury  in  Thuringian  glass  thermometer  ;  the 
specific  gravity  of  the  absolute  alcohol  being  .79391. 

Hi 
IK 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Specific  gravity  at  15°.  56  C.  in  terms  of  water  at  same  temperature. 

0 

10 

20 

30 
40 

50 

60 

g 

90 

I.OOOOO 
.98657 
.97608 
.96541 
•9SI85 

0-93445 

•9r358 
.89010 

•86395 
.83400 

.99847 
•98543 
•97507 
.96421 
.95029 

•93250 

35$ 

.86116 
.83065 

.99699 
.98432 
.97406 
.96298 
.94868 

•93052 
.90907 
.88511 

•85»33 
.82721 

•99555 
.98324 

•97304 
.96172 
.94704 

.92850 
.90678 
.88257 

.85547 
.82365 

•99415 
.98218 
.97201 
.96043 
•94536 

.92646 

•90447 
.88000 
.85256 
.81997 

.99279 
.98114 
.97097 
.95910 
.94364 

.92439 
.90214 
.87740 
.84961 
.81616 

.99147 
.9801  1 
.96991 

•95773 
.94188 

.92229 

•87477 
.84660 
.81217 

.90019 
.97909 
•96883 
•95632 
.94008 

.92015 
.89740 
.87211 

iSoSoo 

•98893 
.97808 
.96772 

•95487 
.93824 

.91799 
.89499 

.86943 
.84044 
•80359 

.98774 
.97708 
.96658 
•95338 
•93636 

.91580' 
.89256 
.86670 
.83726 
.79891 

*  Fownes,  "Phil.  Trans.  Roy.  Soc."  1847. 
t  "  Pogg.  Ann."  vol.  138,  1869. 


SMITHSONIAN  TABLES. 


TABLE  78.  99 

DENSITY  OF  AQUEOUS  METHYL  ALCOHOL.* 

Densities  of  aqueous  methyl  alcohol  at  o°  and  15.56  C.,  water  at  4°  C.  being  taken  as  100000.  The  numbers  in  the 
columns  a  and  b  are  the  coefficients  in  the  equation  pt  =:  PO  —  at  —  bf1  where  pt  is  the  density  at  temperature  i. 
This  equation  may  be  taken  to  hold  between  o°  and  20°  C. 


Percent- 

Density 

Density 

Percent- 

Density 

Density 

age  of 
CH40. 

at 
o°C. 

at 
i5°.56C. 

a 

6 

age  of 
CH4O. 

at 
o°C. 

at 
IS°.S6  C. 

a 

0 

I 

99987 
99806 

99907 
99729 

—6.0 

—  5-4 

0.705 

50 

92873 
92691 

9|8|S 

65.41 
66.19 

2 

99631 

99554 

-4.8 

.681 

52 

92507 

91465 

66.95 

3 

99462 

99382 

—  3-9 

.670 

53 

92320 

91267 

67.68 

4 

99299 

99214 

—  3-0 

•659 

54 

92130 

91066 

68.39 

5 

99142 

99048 

—  2.2 

0.648 

55 

91938 

90863 

69.07 

6 

98990 

98893 

—  1.2 

.634 

56 

91742 

90657 

69.72 

I 

98701 

98726 
98569 

—  0.2 
+  0-9 

.621 
.609 

I 

91S44 
9r343 

90450 
90239 

70.35 
70.96 

9 

98563 

98414 

2.1 

.596 

59 

9OO26 

71-54 

10 

ii 

98429 
98299 

98262 
98111 

a 

0.581 
•569 

60 

61 

90917 
90706 

89798 
89580 

71.96 
72.37 

12 

98171 

97962 

6.2 

-552 

62 

90492 

89358 

72.91 

13 

98048 

97814 

7-8 

.536 

63 

90276 

891  33 

73-45 

14 

97926 

97668 

9-5 

•5*9 

64 

90056 

88905 

73-98 

15 

97806 

97523 

II.O 

0.500 

65 

89835 

88676 

74-51 

16 

97689 

97379 

12-5 

.480 

66 

89611 

88443 

75-05 

17 
18 

97573 
97459 

97235 
97093 

14-5 

1  6.2 

.461 
.440 

68 

89384 
89154 

88208 
87970 

75-57 
76.10 

19 

97346 

96950 

18.3 

.420 

69 

88922 

87714 

76.62 

20 

97233 

96808 

2O.O 

0.398 

70 

88687 

87487 

77-H 

21 

97120 

96666 

22.2 

•373 

71 

88470 

87262 

77-66 

22 

97007 

96524 

24-3 

•350 

72 

88237 

87021 

78.18 

23 

96894 

96381 

26.4 

.321 

73 

88003 

86779 

78.69 

24 

96780 

96238 

29.0 

.291 

74 

87767 

86535 

79.20 

25 

26 

96665 
96549 

96093 
95949 

31-3 

33-8 

0.261 
.230 

75 

76 

87530 
87290 

86290 
86042 

79.71 
80.22 

27 

96430 

95802 

36.0 

.191 

77 

87049 

85793 

80.72 

28 

96310 

95655 

38.8 

78 

86806 

85542 

81.23 

29 

96187 

95506 

41.1 

!io6 

79 

86561 

85290 

8i.73 

Equation  pt  =  Po  —  <** 

80 

81 

86314 
86066 

85035 

82.22 

30 

96057 

95367 

44-36 

82 

OvAJUw 

85816 

84521 

83.21 

31 

95921 

95211 

45-66 

83 

85564 

84262 

83.70 

32 

95783 

95053 

46.93 

84 

85310 

84001 

84.19 

33 

95643 

94894 

48.17 

34 

95500 

94732 

49-39 

85 

85053 

83738 

84.67 

86 

84798 

83473 

85.16 

35 

95354 

94567 

50.58 

87 

83207 

85.64 

36 

95204 

94399 

4 

88 

84278 

82938 

86.12  • 

95051 

94228 

5^89 

2 

89 

84015 

82668 

86.59 

38 

94895 

94055 

54-oi 

s 

39 

94734 

93877 

55-io 

1 

90 

91 

83751 
83485 

82396 
82123 

87.07 
87-54 

40 

94571 

93697 

56-16 

92 

83218 

81849 

88.01 

41 

94400 

935  ro 

57-20 

•<> 

93 

82948 

81572 

88.48 

42 

94239 

93335 

58.22 

a 

94 

82677 

81293 

88.94 

43 
44 

94076 
939" 

93155 
92975 

59-20 
60.17 

5 

95 

82404 

81013 

89.40 

96 

82129 

80731 

89.86 

45 

93744 

92793 

61.10 

81853 

80448 

90.32 

46 

93575 

92610 

62.01 

98 

81576 

80164 

90.78 

47 

93403 

92424 

62.90 

99 

81295 

79872 

91.23 

48 

93229 

92237 

63.76 

49 

93052 

92047 

64.60 

100 

81015 

79589 

91.68 

*  Quoted  from  the  results  of  Dittmar  &  Fawsitt,  "  Trans.  Roy.  Soc.  Edin."  vol.  33. 

u  i-ruertu  i  •  u     T"  A  e»  i   r-m 


100 


TABLE  79. 


VARIATION   OF  THE    DENSITY   OF  ALCOHOL   WITH   TEMPERATURE, 


(a)  The  density  of  alcohol  at  t°  in  terms  of  water  at  4°  is  given*  by  the  following  equation  : 

dt—  0.80025  —  0.0008340*  —  00000029*2. 

From  this  formula  the  following  table  has  been  calculated. 

0 

Density  or  Mass  in  grammes  per  cubic  centimetre. 

d 

5 

H 

0 

1 

2 

3 

4 

5 

6 

7              8 

9 

o 

.80625 

.80541 

.80457 

.80374 

.80290 

.80207 

.80123 

.80039     .79956 

.79872 

10 

•79788 

.79704 

.79620 

•79535 

•79451 

•79367 

.79283 

.79198      .79114 

.79029 

20 

•78945 

.78860 

•78775 

.78691 

.78606 

.78522 

•78437 

.78352      .78267 

.78182 

30 

.78097 

.78012 

•77927 

.77841 

•77756 

.77671 

•77585 

.77500     .77414 

.77329 

(b)  Variations  with  temperature  of  the  density  of  water  containing  different  percentages  of  alcohol.    Water 
at  4°  C.  is  taken  as  unity,  t 

Percent- 

Density  at  temp.  C. 

Percent- 

Density  at  temp.  C. 

alcohol  by 
weight. 

0° 

10° 

20° 

30° 

alcohol  by 
weight. 

0° 

10° 

20° 

30° 

0 

0.99988 

0.99975 

0.99831 

o.9< 

)579 

50 

0.92940 

0.92182 

0.91400 

0.90577 

5 

10 

•99135 
.98493 

•99113 
.98409 

.9f945 
•98195 

.97892 

& 

.91848 
.90742 

91074 
89944 

•90275 
.89129 

.89456 
.88304 

15 

20 

•97995 

.97566 

.97816 
.97263 

877 

.97142 
.96413 

65 
70 

89595 
88420 

88790 
.87613 

.97961 
.86781 

.87125 
•85925 

25 

30 

35 
40 

0.97115 
.96540 
•95784 

•94939 

0.96672 

.95998 

.95*74 
•94255 

0.96l85 
.95403 

•945  1  4 
-93511 

0.95628 
•94751 
.93813 
.92787 

75 

80 

85 
90 

0.87245 
.86035 
.84789 
.83482 

0.86427 

.85215 
.83967 
.82665 

0.85580 
.84366 
.83115 
.8l80I 

0.84719 

•83483 
.82232 
.80918 

45 

•93977 

•93254 

.92493 

.91710 

95 

.82119 

.81291 

.80433 

•79553 

50 

0.92940 

0.92182 

0.91400 

0.90577 

100 

0.80625 

0.79788 

0.78945 

0.78096 

*  Mendelejeff,  "Pogg.  Ann."  vol.  138. 

t  Quoted  from  Landolt  and  Bornstein,  "  Phys.  Chem.  Tab."  p.  359- 


SMITHSONIAN  TABLES. 


30» 


101 


VELOCITY  OF 


iW  SOLiDS. 


The  numbers  given  in  this  table  refer  to  the  velocity  of  sound  along  a  bar  of  the  substance,  and  hence  depend  on  the 
Young's  Modulus  of  elasticity  of  the  material.  The  elastic  constants  of  most  of  the  materials  given  in  this  table 

^  vary  through  a  somewhat  wide  range,  and  hence  the  numbers  can  only  be  taken  as  rough  approximations  to  the 
velocity  which  may  be  obtained  in  any  particular  case.  When  temperatures  are  not  marked,  between  10°  and  20° 
is  to  be  understood. 


Substance. 

Temp.  C. 

Velocity  in 
metres  per 
second. 

Velocity  in 
feet  per 
second. 

Authority. 

Metals:  Aluminum 

0 

5IQ4 

16746 

Masson. 

Brass          .        . 

_ 

35°° 

11480 

Various. 

Cadmium  . 

•    - 

2307 

7570 

Masson. 

Cobalt 

— 

4724 

15506 

M 

Copper 

20 

3560 

11676 

Wertheim,] 

"           .        . 

100 

3290 

I0800 

a 

"            .        . 

200 

2950 

9696 

" 

Gold  (soft) 

2O 

1743 

5717 

H 

"     (hard) 

_ 

2IOO 

6896 

Various. 

Iron  and  soft  steel 

_ 

5000 

16410 

«< 

Iron   ... 

20 

5130 

16820 

Wertheim. 

"... 

100 

5300 

17390 

N 

200 

4720 

15480 

"   cast  steel     . 

20 

4990 

16360 

"      '*      " 

200 

4790 

I57IO 

Lead  ... 

2O 

1227 

4026 

Magnesium 

Nickel 

_ 

4002 

4973 

15106 
16320 

Melde. 
Masson. 

Palladium  . 

— 

3^0 

10340 

Various. 

Platinum    . 

20 

2690 

8815 

Wertheim. 

"            .        . 

100 

2570 

8437 

« 

"                                     . 

200 

2460 

8079 

« 

Silver 

2O 

2610 

8553 

« 

100 

2640 

8658 

H 

Tin     .        ! 

- 

2500 

8200 

Various. 

Zinc    ... 

— 

3700 

12146 

" 

Various:  Brick 

- 

11980 

Chladni. 

Clay  rock 

— 

3480 

11426 

Gray  &  Milne. 

Cork 

— 

500 

1640 

Stefan. 

Granite     . 

- 

3950 

12960 

Gray  &  Milne. 

Marble     . 

— 

3810 

12500 

" 

Paraffin     . 

15 

*3°4 

4280 

Warburg. 

Slate         .        . 
Tallow      .     •  . 

16 

4510 
390 

14800 
1280 

Gray  &  Milne. 
Warburg. 

Tuff. 

— 

2850 

9350 

Gray  &  Milne. 

j-c,                             \  from 

_ 

5000 

16410 

Various. 

Glass        .        *       i  to 

- 

6000 

19690 

Ivory        .... 
Vulcanized  rubber            ) 

0 

3OI3 

54 

177 

Ciccone  &  Campanile. 
Exner. 

(black)  f 

;;        ;;  (red)  . 

0 

I 

102 
226 

« 

70 

34 

iir 

*  *    * 

Wax         .        .        .        ! 

880 

2890* 

Stefan. 

"           .... 

20 

441 

1450- 

««   ' 

Woods  :  Ash,  along  the  fibre  . 

- 

4670 

Wertheim. 

"    across  the  rings 

— 

1390 

4570 

"    along  the  rings 

- 

1260 

4140 

Beech,  along  the  fibre 
"      across  the  rings     . 

_ 

3340 
1840 

10960 
6030 

"      along  the  rings 

— 

1415 

4640 

Elm,  along  the  fibre 
"      across  the  rings 

_ 

4120 
1420 

'3516 

4665 

"      along  the  rings 

- 

1013 

3324 

Fir,  along  the  fibre  . 

— 

4640 

15220 

Maple 
Oak              " 

"" 

4110 
3850 

13470 
12620 

Pine 

— 

3320 

10900 

Poplar 

— 

4280 

14050 

Sycamore    ' 

" 

4460 

14640 

SMITHSONIAN  TABLES. 


102 


•TABLE  81 . 
VELOCITY  OF  SOUND  IN  LIQUIDS  AND  GASES, 


Substance. 

Temp.  C. 

Velocity  in 
metres  per 
second. 

Velocity  in 
feet  per 
second. 

Authority. 

Liquids  :  Alcohol,  95% 

I2?5 

1241. 

4072. 

Dorsing,  1908. 

« 

20.5 

1217. 

3980. 

Ammonia,  cone.   .        . 

1  6. 

I663. 

5456- 

Benzine         .        .        . 

17- 

1166. 

3826. 

Carbon  bisulphide 

IS- 

1161. 

3809. 

Chloroform  . 

iS- 

983- 

3225. 

Ether    .... 

iS- 

1032. 

3386. 

NaCl,  10%  sol.      . 

iS- 

1470. 

4823. 

"      15%  " 

iS- 
iS- 

1530. 
1650. 

5020. 
5414. 

Turpentine  oil      . 

iS- 

1326. 

4351- 

Water,  air-free 

13- 

1441. 

4728. 

«       ««     <( 

19- 

1461. 

4794- 

«       «     « 

31- 

i  SOS- 

4938- 

"      Lake  Geneva   . 

9- 

^S- 

4708. 

Colladon-Sturm. 

"      Seine  river 

IS- 

1437- 

4714. 

Wertheim. 

«          «        u 

u            «          « 

Gases  :  Air,  dry,  CO2-free  . 

£ 

0. 

1528. 
1724. 
33L78 

5013- 
io88.'S 

M 

<« 

Rowland. 

«     « 

0. 

33I-36 

1087.1 

Violle,  1900. 

"     "     CCvfree  '.        '• 

0. 

33r-92 

1089.0 

Thiesen,  1908. 

"       i  atmosphere 

o. 

33*-7 

1088. 

Mean. 

"     25         " 

0. 

332.0 

1089. 

"      (Witkowski). 

50         " 

0. 

3347 

1098. 

«<                <« 

100                        .         • 

0. 

350.6 

1150. 

«                     u 

20. 

•J44. 

1129. 



100. 

386. 

1266. 

Stevens. 

.... 

500. 

553- 

1814. 

H 

IOOO. 

7OO. 

22Q7. 

«( 

Ammonia 

0. 

/   ^*** 

4IS- 

••:?/> 

1361. 

Masson. 

Carbon  monoxide  .        •—- 

0. 

337-1 

1106. 

Wullner. 

«             « 

0. 

3374 

1107. 

Dulong. 

"       dioxide 

0. 

258.0 

846. 

Brock  endahl,  1906. 

"       disulphide  . 

0. 

189. 

606. 

Masson. 

Chlorine  .... 

o. 

206.4 

677. 

Martini. 

M 

0. 

205-3 

674- 

Strecker. 

Ethylene. 
Hydrogen 

0. 
0. 

3i4. 
1269.5 

1030. 
4165. 

Dulong. 

M 

"       .        .        .        • 

0. 

1286.4 

4221. 

Zoch. 

Illuminating  gas 
Methane  .... 

0. 

o. 

490.4 
432- 

1609. 
1417. 

M 

Masson. 

Nitric  oxide     . 

0. 

32S- 

1066. 

H 

Nitrous  oxide  .    .    . 

o. 

26i.8 

859- 

Dulong. 

Oxygen    .... 
Vapors:  Alcohol 

0. 
0. 

317-2 
230.6 

1041. 
756. 

Masson. 

Ether    .... 

o. 

179.2 

588. 

«« 

Water  .... 

0. 

401. 

I3r5- 

« 

4« 

100. 

404.8 

1328. 

Treitz,  1903. 

«( 

130. 

424.4 

1392. 

H 

SMITHSONIAN  TABLES. 


TABLES  82-83. 
MUSICAL  SCALES. 


103 


The  pitch  relations  between  two  notes  may  be  expressed  precisely  (i)  by  the  ratio  of  their  vibration  frequencies; 
(2)  by  the  number  of  equally-tempered  semitones  between  them  (E.  S.);  also,  less  conveniently,  (3)  by  the  common 
logarithm  of  the  ratio  in  (i);  (4)  by  the  lengths  of  the  two  portions  of  the  tense  string  which  will  furnish  the  notes; 
and  (5)  in  terms  of  the  octave  as  unity.  The  ratio  in  (4)  is  the  reciprocal  of  that  in  (i);  the  number  for  (5)  is  i/ia  of 
that  for  (2);  the  number  for  (2)  is  nearly  40  times  that  for  (3). 

Table  82  gives  data  for  the  middle  octave,  including  vibration  frequencies  for  three  standards  of  pitch;  a  =  435  double 
vibrations  per  second,  is  the  international  standard  and  was  adopted  by  the  American  Piano  Manufacturers'  Associa- 
tion. The  "just-diatonic  scale"  of  C-major  is  usually  deduced,  following  Chladni,  from  the  ratios  of  the  three  perfect 
major  triads  reduced  to  one  octave,  thus:  4:5:6 

F  A  C  E  G       '     B  D 

16  20  24  30  36  45  54 

24     27     30    32     36    40    45     48 

Other  equivalent  ratios  and  their  values  in  E.  S.  are  given  in  Table  83.  By  transferring  D  to  the  left  and  using  the 
ratio  10  :  12  : 15  the  scale  of  A-minor  is  obtained,  which  agrees  with  that  of  C-major  except  that  D  =  26  2/3.  Nearly  the 
same  ratios  are  obtained  from  a  series  of  harmonics  beginning  with  the  eighth;  also  by  taking  12  successive  perfect 
or  Pythagorean  fifths  or  fourths  and  reducing  to  one  octave.  Such  calculations  are  most  easily  made  by  adding  and 
suotracting  intervals  expressed  in  E.  S.  The  notes  needed  to  furnish  a  just  major  scale  in  other  keys  may  be  found 
by  successive  transpositions  by  fifths  or  fourths  as  shown  in  Table  83.  Disregarding  the  usually  negligible  difference 
of  o.oa  E.  S.,  the  table  gives  the  24  notes  to  the  octave  required  in  the  simplest  enharmonic  organ;  the  notes  fall  into 
pairs  that  differ  by  a  comma,  0.22  E.  S.  The  line  "mean  tone"  is  based  on  Dom  Bedos'  rule  for  tuning  the  organ 
(1746).  The  tables  have  been  checked  by  the  data  in  Ellis'  Helmholtz's  "Sensations  of  Tone." 

TABLE  82. 


Interval. 

Ratios. 

Logarithms. 

Number  of  Vibrations  per  second. 

Beats 

Tem- 
pered. 

Just. 

Tem- 
pered. 

Just. 

Tem- 
pered. 

Just. 

Just. 

Just. 

Just. 

Tem- 
pered. 

E.  S. 

E.  S. 

E.  S. 

c' 

O 

0. 

1.00 

1.  00000 

0.0000 

o.ooooo 

^ 

264 

258.7 

258.7 

1.50 

I 

.05926 

.02509 

274.0 

d' 

2 

2.04 

I.I25 

.12246 

.05115 

.05017 

288 

297 

291.0 

290.3 

1.68 

3 

.18921 

.07526 

307.6 

e' 

4 

3.86 

1.25 

.25992 

.09691 

.10034 

320 

330 

323.4 

325-9 

I.89 

f 

i 

4.98 

i-33 

.33484 
.41421 

.12494 

•12543 

.15051 

341-3 

352 

344-9 

345-3 
365-8 

2.00 

g' 

7 

7.02 

1.50 

.49831 

.17609 

.17560 

384 

396 

388 

387.5 

2.25 

8 

.58740 

.20069 

410.6 

a' 

9 

10 

8.84 

1.67 

.68179 
.78180 

.22185 

.25086 

426.7 

440 

431-1 

435-0 
460.9 

2.52 

b' 

ii 

10.88 

I.87S 

.88775 

.27300 

.27594 

480 

495 

485.0 

488.3 

2.83 

c" 

12 

I2.OO 

2.OO 

2.OOOOO 

.30103 

.30103 

5I2 

528 

S'7-3 

517.3 

3-00 

TABLE  83. 


Key  of 

C 

D 

E 

F 

G 

A 

- 

B 

C 

•7   8« 

r# 

1.14 

3.18 

5.00 

6.12 

8.16 

9.98 

12.02 

f   frS 

\-ftf 

0.92 

2.96 

4.78 

5-90 

7-94 

9.76 

II.80 

(\  " 

Ftf 

1.14 

2.96 

5.00 

6.12 

8.16 

9.98 

It.  TO 

o 

X^IT 

0.92 

2.74 

4.78 

5-90 

7-94 

9.76 

10.88 

Su 

3 

1.14 

2.96 

4.08 

6.12 

7-94 

9.98 

II.IO 

0.92 

2.74 

3-86 

5.90 

7.72 

9.76 

10.88 

A     " 

0.92 

2.96 

4.08 

6.12 

7-94 

9.06 

II.IO 

4 

0.70 

a.  74 

3-86 

5-90 

7.72 

8.84 

10.88 

3M 

0.92 

2.04 

4.08 

5-90 

7-94 

9.06 

II.IO 

0.70 

1.82 

3.86 

5.68 

7.72 

8.84 

10.88 

2    « 

D 

0.92 

2.04 

4.08 

5.90 

7-02 

9.06 

10.88 

ll 

G 

0.00 

2.04 

3-86 

5.90 

7.02 

9.06 

10.88 

I2.OO 

C 

o.oo 

2.04 

3-86 

4-98 

7.02 

8.84 

10.88 

I2.OO 

Ib 

F 

o.oo 

1.82 

3-86 

4.98 

7.02 

8.84 

9.96 

12.00 

2bS 

BE> 

0.00 

1.82 

2.94 

4.98 

6.80 

8.84 

9.96 

12.00 

3" 

Ei> 

-.22 

1.82 

2.94 

4.98 

6.80 

7.92 

9.96 

11.78 

4" 

Ai> 

-.22 

0.90 

2.94 

4.76 

6.80 

7.92 

9.96 

11.78 

*•" 

Db 
G!> 

-.22 

0.90 
0.90 

2.94 
2.72 

4.76 
4.76 

5-88 

5.88 

7.92 
7.92 

9-74 
9-74 

10.86 

11.78 

7" 

Ci> 

0.90 

2.72 

3-84 

5.88 

7.70 

9-74 

10.86 

Harmonic  Series 

8 

0.0 

/'.7'\ 
\i.o5/ 

9 
2.04 

/  19  \ 
UgS/ 

10 

3-86 

(2I) 
\4-70/ 

II 

5.51 

12 

7.02 

/*5\ 
\7.73/ 

8.'43, 

14 
9.69 

10.88 

16 

12.00 

Cycle  of  fifths 
Cycle  of  fourths 
Mean  tone 

O.O 
O.O 

0.0 

I.I4 

0.90 
0.76 

2.04 
1.  80 

!-93 

3-'8 

2.94 

3-" 

4.08 
3.84 
3-86 

5.22 
4.98 
5-03 

6.12 

5.88 
5-79 

7.02 
6.78 

8.16 
7.92 
772 

9.06 
8.82 
8.90 

10.20 
9.96 
IO.O7 

II.IO 

10.86 
10.83 

12.24 
11.76 

I2.OO 

Equal  7  step 

0.0 

1.71 

3-43 

5-M 

^:86. 

8-57 

IO.29 

12.00 

SMITHSONIAN  TABLES. 


IO4 


TABLE  84.    ACCELERATION  OF  GRAVITY. 

For  Sea  Level  and  Different  Latitudes. 

This  table  has  been  calculated  from  the  formula  g^  =•£&  [i  —  .002662  cos  2<f>]*  where  $  is  the  latitude. 


Lati- 
tude <£. 

g 

in  cms.  per 
sec.  per  sec. 

Log. 

ff 

in  inches  per 
sec.  per  sec. 

Log. 

ff 

in  feet  per 
sec.  per  sec. 

Log. 

0° 

977.989 

2-990334 

385-034 

2.585498 

32.0862 

1.506318 

5 

8.029 

0352 

.050 

5517 

.0875 

6336 

10 

.147 

0404 

.096 

5570 

.0916 

6388 

15 

•339 

0490 

•173' 

5655 

.0977 

6474 

20 

0605 

•275 

5771 

.1062 

6590 

25 

978.922 

2.990748 

385.402 

2.585914 

32.1168 

1.506732 

30 

9-295 

0913 

.548 

6079 

.1290 

6898 

3i 

•374 

0949 

.580 

6114 

.1316 

6933 

32 
33 

•456 
•538 

0985 
IO2I 

.6l2 
.644 

6150 
6187 

•1343 
•1370 

6969 
7005 

34 

979.622 

2.991059 

385-677 

2.586224 

32.1398 

I-507043 

35 

.707 

1096 

.711 

6262 

.1425 

7080 

36 

•793 

"35 

•745 

6300 

•1454 

7119 

37 

.880 

"73 

•779 

6339 

.1490 

7167 

38 

.968 

1212 

•813 

6377 

.1511 

7196 

39 

980.057 

2.991251 

385-849 

2.586417 

32.1540 

1.507236 

40 

.147 

1291 

.884 

6457 

•1570 

7275 

41 

•237 

1331 

.919 

6496 

.1607 

7325 

42 

•327 

1372 

•955 

6537 

.1630 

7356 

43 

.418 

I4II 

.990 

6577 

.1659 

7395 

44 

980.509 

2.991452 

386.026 

2.586617 

32.1688 

1.507436 

45 
46 

.600 
.691 

1492 
1532 

.062 
.098 

6657 
6698 

.1719 

.1748 

7476 
75*6 

47 

.782 

J573 

•134 

6738 

.1778 

7557 

48 

•873 

1613 

.170 

6778 

.1808 

7597 

49 

980.963 

2.991653 

386.205 

2.586818 

32.1838 

1-507637 

50 

1-053 

i693 

.241 

6858 

.1867 

7677 

5i 

•143 

1732 

.276 

6898 

.1896 

7716 

52 

.231 

1772 

•3" 

6937 

.1924 

7756 

53 

.318 

1810 

•345 

6975 

•J954 

7794 

54 

981.407 

2.991849 

386.380 

2.587014 

32.1983 

1-507833 

55 

•493 

1887 

.414 

7053 

.2011 

7871 

56 

57 

£ 

J925 
1962 

•447 
.480 

7090 
7127 

•2039 
.2067 

7909 
7946 

58 

•744 

1998 

•5J3 

7164 

.2094 

7983 

59 

981.825 

2.992034 

386.545 

2.587200 

32.2121 

1.508018 

60 

•905 

2070 

•576 

7235 

.2147 

8054 

i  65 

2.278 

2234 

•723 

7400 

.2276 

8229 

70 
75 

.600 
.861 

2377 
2492 

.849 
•952 

7542 
7657 

•2375 
.2460 

8361 
8476 

80 

983-053 

2.992577 

387.028 

2.587742 

32.2523 

1.508561 

!  85 

.171 

2629 

.074 

7794 

.2562 

8613 

90 

.210 

2646 

.090 

7812 

•2575 

8631 

*  The  constant  .002662  is  based  on  Harkness'  data  (Solar  Parallax  and  Related  Constants,  Washington,  1891). 
The  acceleration  of  gravity  for  any  latitude  <f>  and  elevation  above  sea  level  h  is  very  nearly  expressed  by  the  equation 

g$=sv&  (i— -002662  cos  2<t>)  [_l~ji(l~~Tb)j* 

where  R  is  the  earth's  radius,  8  the  density  of  the  surface  strata,  and  A  the  mean  density  of  the  earth.  When  5=o 
we  get  the  formula  for  elevation  in  air.  For  ordinary  elevations  on  land  —  is  nearly  J,  which  gives  for  the  correction 
at  latitude  45°  for  elevated  portions  of  the  earth's  surface 

eu-^— 98o.6X^-  =  1225.75—  cm.  per  sec.  per  sec. 
4R  4/c  R 

=386.062  X  5*  =482.562—  in.  per  sec.  per  sec. 
4R  R 

=32.1719X^=40.2149  —  feet  per  sec.  per  sec. 
+R  R 

This  gives  per  100  feet  elevation  a  correction  of 

.00588  cm.  per  sec.  per  sec.   ) 

.00232  in.  per  sec.  per  sec.      >  diminution. 

.000193  feet  per  sec.  per  sec.  ) 
SMITHSONIAN  TABLES. 


TABLE  85. 
GRAVITY. 


105 


In  this  table  the  results  of  a  number  of  the  more  recent  gravity  determinations  are  brtmght  together.  They  serve  to 
show  the  degree  of  accuracy  which  may  be  assumed  for  the  numbers  in  Table  112.  In  general,  gravity  is  a  little 
lower  than  the  calculated  value  for  stations  far  inland  and  slightly  higher  on  the  coast  line. 


Place. 

Latitude. 

N.  +,  S.  —  . 

Elevation 
in  metres. 

Gravity,   ^ 
sec2 

Refer- 
ence. 

Observed. 

Reduced  to 
sea  level. 

Singapore   .    .    •     

1°    I7' 
-7     56 
—  7     57 
-8    49 

—  10      00 

13  04 

-IS    55 
-15    57 
20    43 

20      52 
20      56 
21       18 
32      23 

-33    52 
—  33    56 
35    4i 
—  36    S2 
37     20 
37     20 
37    47 
37    47 
38    53 
39    54 
39    58 
40    27 
40    28 
40    44 
40    46 
41     49 
42    49 
45    3i 

46      12 
46      12 

46    57 
47     23 
48    50 
51     28 
52    3° 
54    34 
55    59 
56    28 
57    03 
57    07 
58    18 
59    I0 
59    32 

14 

681 
46 

.2 

18 
10 

533 
3001 

3 
117 

3 

2 

43 
ii 
6 

43 
1282 
1282 
114 
114 
10 
1645 

122 
65I 
348 
II 
1288 
I65 

450 
100 

405 
405 

53 

67 

i 

,  0 

8 

12 

5 
5 
4 

97,8.08 
978.25 
978.10 
978.15 
978-37 
978.18 
978.67 

978.53 
978.28 
978.86 
978.91 
978.97 
979-77 
979-68 
979.62 

979-95 
979-68 
979.66 
979-68 
979.96 
980.02 
980.  1  1 
979-68 
980.12 
93o.o8 
980.09 
980.27 
979.82 
980.34 
980.34 
980.73 
980.58 
980.60 
980.61 
980.67 
980.96 
981.20 
981.26 
98146 
981.51 
981.60 
981.69 
981.67 
981.74 
981.82 
981.83 

978.08 
97f.25 
978.23 
978.16 

978.37 
978.18 
978.67 

978.59 
978.85 
978.86 

978.93 
978.97 
979.77 
979.69 
979-62 

979-95 
979.69 
979.91 
979.92 
979.98 
980.04 
980.11 
979.98 
980.14 
980.20 
980.15 
980.27 
980.05 
980.37 
980.42 
980.75 
980.64 
980.66 
980.69 
980.74 
980.97 
981.20 
981.27 
981.46 
981.51 
981.60 
981.69 
981.67 
981.74 
981.82 
981.83 

I 

2 

2 
2 

3 

2 
2 
2 
3 

3 
3 
3 

2 
I 

2 

I 
I 

4 
5 
4 
5 
4 

6 
6 

4 
5 
5 
7 

1 

9 
9 

§ 

8 
8 
4 
4 
4 
4 
^ 
4 
4 
4 

Georgetown,  Ascension    .... 
Green  Mountain,  Ascension  .    .     . 
Loanda  Angola 

Bridgetown,  Barbadoes     .... 
Jamestown,  St,  Helena     .... 
Longwood,            "            .... 
Pakaoao,  Sandwich  Islands  .     .     . 
Lahaina,           "               "... 
Haiki,              "              "... 
Honolulu,        "              "... 
St.  Georges,  Bermuda      .... 

Cape  Town      

Tokio.  Japan  

Auckland,  New  Zealand   .... 

Mount  Hamilton,  Cal.  (Lick  Obs.) 
«              «            «i            « 

San  Francisco,  Cal       

Washington,  D.  C.*     
Denver,  Colo  

York,  Pa  

Hoboken,  N  J  

Salt  Lake  City,  Utah  

Chicago,  111  

Pampaluna  Spain    ...... 

Montreal  Canada    .    •         ... 

«                « 

Berne               "              

Zurich              "               

Burroughs  Bay,  Alaska 
Wrangell, 
Sitka, 
St.  Paul's  Island,    " 
Juneau,                     " 
Pyramid  Harbor,    " 
Yakutat  Bay, 

i  Smith  :  "  United  States  Coast  and  Geodetic  Survey  Report  for  1884,"  App.  14. 
2  Preston  :  "  United  States  Coast  and  Geodetic  Survey  Report  for  1890,"  App.  12. 
3  Preston  :  Ibid.  1888,  App.  14. 
4  Mendenhall  :   Ibid.  1891,  App.  15. 
5  Defforges  :  "  Comptes  Rendus,"  vol.  118,  p.  231. 
6  Pierce  :  "U.  S.  C.  and  G.  S.  Rep.  1883,"  App.  19. 
7  Cebrian  and  Los  Arcos  :  "Comptes  Rendus  des  Seances  de  la  Commission  Perma- 
nente  de  1'Association  Geodesique  International,"  1893. 
8  Pierce:  "  U.  S.  C.  and  G.  S.  Report  1876,  App.  15,  and  1881,  App.  17." 
9  Messerschmidt  :  Same  reference  as  7. 

»  For  references  1-4,  values  are  derived  by  comparative  experiments  with  invariable  pendulums,  the  value  for 
Washington  taken  as  980.111.    For  the  latter  see  Appendix  5  of  the  Coast  and  Geodetic  Survey  Report  for  1901. 
SMITHSONIAN  TABLES. 


io6 


TABLE  86. 


SUMMARY  OF   RESULTS  OF  THE  VALUE  OF  GRAVITY  (g)  AT  STATIONS 
IN    THE    UNITED   STATES   AND   ALASKA.* 


Station. 

Latitude. 

Longitude. 

Elevation. 

g 

observed. 

Calais,  Me  

o      /      // 
45  ii  ii 

o     t      n 
67  16  C4 

Metres. 
l8 

cm./sec.a 
080.670 

4.2   21    77 

71    O  7    CO 

080  7OC 

•4   -*1    jj 

42    22   40 

7  i   07   A  C 

14 

y°u<jy5 

080  7Q7 

42    I  6   2Q 

71   48  20 

I7O 

you-jy/ 

980  727 

New  York,  N.  Y  

4O  4o   27 

77    C7   47 

980  266 

4O   2O    C7 

/J   O/   4J 
74    7Q   28 

•3 

Philadelphia,  Pa  

V       ^rW        W 

TO     C7    OO 

7  c    ii    40 

l6 

you.i// 

080  IQC 

Ithaca,  N.  Y  

42   27   O4 

7O  2Q  OO 

247 

you.iy.3 
QftO  2QQ 

70   17    SO 

76    77    7O 

7O 

yow.^yy 
980  O9O 

Washington,  C.  &  G.  S  
Washington,  Smithsonian  .... 
Charlottes  ville,  Va  

3f  53  13 
3§  53  20 
30  02  01 

77  oo  32 
77  oi  32 
78  70  i  6 

Ju 
14 
IO 

166 

98O.III 
980.113 
Q7Q  Q77 

Deer  Park,  Md  

•3Q    2C    O2 

7Q    IQ    CO 

77O 

y/y-yj/ 

Charleston,  S.  C  

72   47    14 

/y  *y  D" 

7Q    C6  O7 

770 

y/y-yj'f 

Q7Q    CJC 

Cleveland,  Ohio  

41    7O  22 

81  76  78 

2IO 

980  240 

Key  West,  Fla  

24   77    77 

81  48  25 

j 

Q78  060 

Atlanta,  Ga.         

7  7  44    c8 

84  27  1  8 

724 

y/o.yvjy 

70  08   2O 

84   2  C   2O 

J-^'t 

24  C 

/yo^j 

080  OO7 

Terre  Haute,  Ind  

70   28  42 

8?    2  7   4Q 

I  CI 

yt«j.<-^/j 
980  071 

Chicago,  111  

41    47    2C 

87    76  O7 

i£ 

Q8o  277 

Madison,  Wis.  (Univ.  of  Wis.)  . 
New  Orleans,  La  
St.  Louis,  Mo  
Little  Rock,  Ark  

43  04  35 
29  56  58 
38  38  03 

74  44    C7 

89  24  oo 

90  04    14 
90    12    I3 
Q2    ID   24 

270 

2 

980.364 
979-323 
980.000 
Q7Q  72O 

700?    CO 

Q4    7^   21 

278 

Q7Q  080 

Galveston,  Tex.  . 
Austin,  Texas  (University)          .        . 
Austin,  Texas  (Capitol)      .... 
Ellsworth,  Kan  

29  18  12 

30   17    II 

30  16  30 

78   47   47 

94  47  29 
97  44  14 
97  44  16 

Q8    17    72 

*i 

170 

4OQ 

979.271 
979.282 
979.287 
Q7Q  Q2  C 

Laredo,  Tex  

27    7O   20 

QQ    71    12 

I2Q 

y/y-y-'O 
Q7o  081 

Wallace,  Kan  

0      J                ~ 

78    C4  44 

IOI    7  C.   2O 

IOOC 

O7Q  7  C4 

Colorado  Springs,  Col  
Denver,  Col  

38  50  44 

7Q   40   76 

104  49  02 
104  c6  cc 

1841 
1678 

979.489 
O7Q  608 

Pike's  Peak,  Col  

38    50   2O 

105  02  02 

42Q7 

078  QC7 

Gunnison,  Col  
Grand  Junction,  Col  

38  32  33 
39  04  09 

78    CQ  27 

I  06  56  02 
108  33  56 
no  09  56 

2340 
1398 
1247 

979-341 
979.632 

Q7Q  O7  C 

44  47    IO 

IIO   20  44 

2386 

Q7Q  808 

Norris  Geyser  Basin,  Wyo. 
Lower  Geyser  Basin,  Wyo. 
Pleasant  Valley  Jet.,  Utah  . 
Salt  Lake  City,  Utah  . 
Ft.  Egbert,  Eagle,  Alaska  . 

44  44  09 
44  33  21 
39  50  47 
40  46  04 
64  47  22 

no  42  02 
no  48  08 

III    00   46 

in  S3  46 

141    12    24 

2276 

2200 
2191 
I322 
174 

979-949 
979.931 
979-511 
979.802 
982.182 

*  All  the  values  in  this  table  depend  on  relative  determination  of  gravity  and  an  adopted  value  for  gravity  at  Wash- 
ington (Coast  and  Geodetic  Survey  Office)  of  980.111.  This  adopted  value  was  the  result  of  the  determination  in 
1900  of  the  relative  value  of  gravity  at  Potsdam  and  at  Washington.  See  footnote  on  previous  page. 

SMITHSONIAN  TABLES. 


TABLES  87-88. 
LENGTH  OF  THE  SECONDS  PENDULUM. 

TABLE  87. -Length  of  Seconds  Pendulum  at  Sea  Level  lor  Different  Latitudes.* 


ID/ 


Lati- 
tude. 

Length 
in  centi- 

Log. 

Length  in 
inches. 

Log. 

Lati- 
tude. 

Length 
in  centi- 

Log. 

Length  in 
inches. 

Log. 

0 

99.0910 

1.996034 

39.0121 

1.591200 

50 

99.4014 

1-997393 

39.1344 

L592558 

5 

.0950 

6052 

•0137 

1217 

55 

•4459 

7587 

.1520 

2753 

10 

.1079 

6104 

.0184 

1270 

60 

.4876 

7770 

.1683 

2935 

IS 

20 

.1265 
.1529 

6190 

6306 

.0261 
•0365 

1356 
I47I 

65 

70 

•5255 
.SS« 

$;5 

.1832 
.1960 

3100 
3242 

25 

99.1855 

1.996448 

39-0493 

1.591614 

75 

99-5845 

I.998I92 

39.2065 

L593358 

3° 

.2234 

6614 

.0642 

1779 

80 

8277 

.2141 

3442 

35 

.2651 

6796 

.0806 

1962 

8S 

.6160 

.8329 

.2188 

3494 

40 

.3096 

6991 

.0982 

2157 

90 

.6200 

8347 

.2204 

35'2 

45 

•3555 

7192 

.1163 

2357 

*  Calculated  from  force  of  gravity  table  by  the  formula  l—g/it*.    For  each  100  feet  of  elevation  subtract  0.000596 
centimetres,  or  0.000235  inches,  or  .0000196  feet. 


TABLE  88.  —  Length  of  the  Seconds  Pendulum.* 


Number 

Correspond- 

determi- 
nation. 

of  obser- 
vation 
stations. 

Range  of  latitude  included  by 
the  stations. 

Length  of  pendulum  in  metres 
for  latitude  <$>. 

ing  length 
of  pendulum 
for  lat.  45° 

Refer- 
ence. 

1799 

1816 
1821 

15 

From- 

-67°o5'to  —  33°  56^ 
-74°53'  "-5i°2i' 
-38°  4C/  "  —  6o°45' 

0.99063  1  +  .005637  Sin2  £ 
0.9907  43+  .005466  sin2  </> 
o.99o88o+.oo534o  sin  2  <j> 

0.993450 
0.993976 

0-99355° 

I 
2 

3 

1825 

25 

"     - 

-79°  50'  "  —i  2°  59' 

0.99097  7  +  .005  1  42  sin  2  ^> 

0.993548 

4 

1827 
1829 

41 

5 

«     ^ 

-79°  50*  «  —51°  35' 
o°  cf  "  +67°04' 

0.99  1  026+  .00507  2  sin  2  <f> 
o.99O555~r".oo5679^^2</* 

0.993562 
0-993395 

i 

1830 

49 

"     +79°  5»'  "  —  5i°35' 

0.99  1017+  .005087  sin  2  4> 

7 

1833 

—       "      — 

0.990941+.  005142  sin2  4> 

0.993512 

8 

1869 
1884 

73 
123 

"     +79°  5°'  "~5I°35/ 
"     4-79°  So'  "-62°  56' 
«     +79°  50"'  -62°  56' 

0.990970+  .005  1  85  sin2  <p 
0.99101  i  +.005105  sin24> 
0.9909  1  8+.OO5262  sin2  4> 

°-993554t 

0.993563 
0-993549 

9 

10 

ii 

Combining  the  above  r< 

0.990910+  .005290  sin2^ 

0-993555 

12 

1  Laplace  r  "Traite  de  Mecanique  Celeste,"  T.  2,  livre  3,  chap.  5,  sect.  42. 

2  Mathieu:  "  Sur  les  experiences  du  pendule;"  in  "  Connaissance  des  Temps  1816." 
Additions,  pp.  314-341,  p.  332. 

3  Biot  et  Arago  :  "  Recueil  d'Observations  geodesiques,  etc."    Paris,  1821,  p.  575. 

4  Sabine :  "  An  Account  of  Experiments  to  determine  the  Figure  of  the  Earth,  etc.,  by 
Sir  Edward  Sabine."    London,  1825,  p.  3^2. 

5  Saigey : _" Comparaison  des  Observations  du  pendule  a  diverses  latitudes;  faites  par 

Mathe- 


MM.  Biot,  Kater,  Sabine,  de  Freycinet,  et  Duperry ; "  in  "  Bulletin  des  Sciences  M; 
matiques,  etc.,"  T.  i,  pp.  31-43,  and  171-184.     Pans,  1827. 

6  Pontecoulant :  "  Theorie  analytique  du  Systeme  du  monde,"  Paris,  1829,  T.  2,  p. 
Airy :  "  Figure  of  the  Earth ; "  in  "  Encyc.  Met."  2d  Div.  vol.  3,  p.  230. 


466. 


PP. 

p.  316. 

10  Fischer :  "  Die  Gestalt  der  Erde  und  die  Pendelmessungen ; "  in  "  Ast.  Nach."  1876, 
col.  87. 

11  Helmert:  "Die  mathematischen  und  physikalischen  Theorieen  der  hoheren  Geo- 
dasie,  von  Dr.  F.  R.  Helmert,"  II.  Theil.    Leipzig,  1884,  p.  241. 

12  Harkness. 


*  The  data  here  given  with  regard  to  the  different  determinations  which  have  been  made  of  the  length  of  the 
seconds  pendulum  are  quoted  from  Harkness  (Solar  Parallax  and  its  Related  Constants,  Washington,  1891). 
t  Calculated  from  a  logarithmic  expression  given  by  Unferdinger. 

SMITHSONIAN  TABLES. 


IOS  TABLE  89. 

MISCELLANEOUS   DATA  WITH  REGARD  TO  THE  EARTH  AND   PLANETS.* 


Length  of  the  seconds  pendulum  at  sea  level  =7=39.012540+0.208268  sin2  finches. 

=3.251045+0.017356  sin2  0  feet. 
=0.9909910+0.005290  sin2  0  metres. 

Acceleration  produced  by  gravity  per  second 

per  second  mean  solar  time      .        .        .  =^=32.086528+0.171293  sin2  0  feet. 

=977.9886+5.2210  sin2  0  centimetres. 


Equatorial  radius  =0=6378206  metres  ; 

3963.225  miles. 
Polar  semi-diameter       =£=6356584  metres  ; 

3949.790  miles. 

Reciprocal  of  flattening=  —  -  =295.0 


a—  b  ^ 

S. 


Square  of  eccentricity   =**=  -^—  =0.006768658 


6378388+18  metres; 
3963-339  miles. 
6356909  metres ; 
3949.992  miles. 

297.0+0.5 

0.0067237+0.0000120. 


Difference  between  geographical  and  geocentric  latitude=  0—0'= 

688.2242//  sin  2  0—1.1482"  sin  4 0+0.0026" sin 60. 

Mean  density  of  the  Earth=5.5247±o.ooi3  (Burgess  Phys.  Rev.  1902). 

Continental  surface  density  of  the  Earth =2.67          \  Harkness 
Mean  density  outer  ten  miles  of  earth's  crust=2.4O  j 

Moments  of  inertia  of  the  Earth;  the  principal  moments  being  taken  as  A,  B,  and  C,  and 
C  the  greater: 

C-A  ,  i 

— — —  =0.00^2652 1  =  — 7 ; 

C  306.259' 

C— -4  =0.00 1064767  Ea*\ 
A  =^=0.32  5029  Eaz-, 
C  =0.326094  £a2; 
where  E  is  the  mass  of  the  Earth  and  a  its  equatorial  semidiameter. 

Length  of  sidereal  year=365.2563578  mean  solar  days; 

=365  days  6  hours  9  minutes  9.314  seconds. 


Length  of  tropical  year=365.242i9987O— 0.0000062124—  — ^-mean  solar  days; 

=365  days  5  hours  48  minutes  (46.069—0.53675-^-^-  J  seconds. 

Length  of  sidereal  month 


:27.32i66i  162— 0.00000026240 —  — days; 


=27  days  7  hours  43  minutes  ( 1 1.524—0.022671 J  seconds. 

Length  of  synodical  month 

,  ,t— 1800, 
=29.530588435-0.00000030696— ^—  days; 

=29  days  12  hours  44  minutes  (2.841—0.026522 —       -  1  seconds. 
Length  of  sidereal  day  =  86164.09965  mean  solar  seconds. 

N.  B. — The  factor  containing/  in  the  above  equations  (the  epoch  at  which  the  values  of 
the  quantities  are  required)  may  in  all  ordinary  cases  be  neglected. 


*  Mostly  from  Harkness,  "  Solar  Parallax  and  Allied  Constants.' 
SMITHSONIAN  TABLES. 


TABLE  89  (continued).  109 

MISCELLANEOUS  DATA  WITH   REGARD  TO  THE  EARTH   AND  PLANETS. 


Masses  of  the  Planets. 
Reciprocals  of  the  masses  of  the  planets  relative  to  the  sun  and  the  mass  of  the  moon 

relative  to  the  Earth. 

Mercury  =  6000000 
Venus     =   408000 
Earth  *    =    329390 
Mars       =  3093500 
Jupiter    =        1047.35 
Saturn     =        3501.6 
Uranus   =      22869 
Neptune  =      19700 

Moon      =  81.45 


Mean  distance  from  earth  to  sun  =  92900000  miles  =  149500000  kilometres. 
Eccentricity  of  the  earth's  orbit  =  e  = 

0.01675104  —  0.0000004180  (f —  1900)  — 0.000000126  (  -         —  V 

Solar  parallax  =  8.7997"  i  °-°°3  (Weinberg,  A.  N.  165,  1904)  ; 
8.807  i  0.0027  (Hinks,  Eros,  7) ; 
8.799  (Samson,  Jupiter  satellites;  Harvard  observations). 
Lunar  parallax  =  3422.68". 

Mean  distance  from  earth  to  moon  =  60.2669  terrestrial  radii; 

=  238854  miles ; 
=  384393  kilometres. 

Lunar  inequality  of  the  earth  =  L  —  6.454". 
Parallactic  inequality  of  the  moon  =  Q  =  124.80". 

Mean  motion  of  moon's  node  in  365.25  days  =  p  =  —  19°  21'  19.6191"  -j-  0.14136"  (  — J 

Eccentricity  and  inclination  of  the  moon's  orbit  =  e2  =  0.05490807. 
Delaunay's  7  =  sin  \  1=  0.044886793. 

7  =5°  08' 43.3S46". 
Constant  of  nutation  =  9.2'. 

Constant  of  aberration  =  20.4962  -J-  0.006  (Weinberg,  1.  c.).t 
Time  taken  by  light  to  traverse  the  mean  radius  of  the  earth's  orbit 

=  498.82  ^  o.i  seconds  (Weinberg) ; 
=  498.64  (Samson). 

Velocity  of  light  =  186330  miles  per  second  (Weinberg) ; 
=  299870  J^  0.03  kilometres  per  second. 
General  precession  =  50.2564"  +  0.000222  (t  —  1900). 
Obliquity  of  the  ecliptic  =  23°  27'  8.26"—  0.4684  (t—  1900). 

Gravitation  constant  =  666.07  X  io~10  cm3/gr.  sec2^  o.i 6  X  io~10. 


«  Earth  -f  moon.  t  Recent  work  of  Doolittle's  and  others  indicates  a  value  not  less  than  20.51. 

SMITHSONIAN  TABLES. 


no 


TABLE  90. 
TERRESTRIAL   MAGNETISM. 


Secular  Change  of  Declination. 

Changes  in  the  magnetic  declination  between  1810,  the  date  of  the  earliest  available  observa- 
tions, and  1910,  for  one  or  more  places  in  each  state  and  territory. 


State. 

Station. 

1810 

1820 

1830 

1840 

1850 

i860 

1870 

1880 

1890 

1900 

1910 

Ala. 

Montgomery 

S.6E 

S.8E 

S.8E 

S.6E 

S-4E 

S.oE 

4-SE 

3-9E 

3.2E 

2.8E 

2.9E 

Alas. 

Sitka 

- 

- 

- 

- 

- 

28.?E 

29.oE 

29-3E 

29-SE 

29-7E 

30.2E 

Kodiak 

- 

- 

- 

- 

- 

26.iE 

25.  6E 

2S.iE 

24.7  E 

24.4E 

24.iE 

Unalaska 

- 

- 

- 

- 

- 

20-4E 

20.  lE 

I9.6E 

19-oE 

I8.3E 

I7-SE 

St.  Michael 

— 

— 

— 

— 

— 

— 

— 

24.7E 

23.iE 

22.  lE 

2I.4E 

Ariz. 

Holbrook 

_ 

_ 

- 

_ 

13.  6E 

I3-7E 

I3.8E 

13  -7  E 

I34E 

I3-5E 

13-  9E 

Prescott 

- 

- 

-  ' 

- 

I3-3E 

I3-5E 

I3-7E 

I3.6E 

I3.SE 

I3-7E 

I4-3E 

Ark. 

Little  Rock 

8.6E 

8.8E 

p.oE 

9.oE 

8.8E 

8.6E 

8.2E 

7.6E 

?.oE 

6.6E. 

6.9E 

Cal. 

Los  Angeles 

I2.IE 

I2.6E 

I3.2E 

I3-6E 

i4.oE 

I4.2E 

I44E 

I4.6E 

I4.6E 

I4-9E 

IS-SE 

San  Jose 

15-oE 

I5-5E 

i6.oE 

I6-4E 

I6.8E 

17.  lE 

I7-3E 

I7-5E 

I7-SE 

17.  8E 

I8.5E 

Cal. 

Redding 

IS-6E 

i6.iE 

I6.6E 

I7.0E 

I7-4E 

17  .8E 

iS.iE 

I8.2E 

I8.3E 

I8.6E 

I9-3E 

Colo. 

Pueblo 

- 

- 

- 

- 

I3.8E 

I3.8E 

I3.8E 

I3-SE 

13-oE 

I2.9E 

I3-3E 

Glenwood  Sp. 

- 

- 

- 

- 

i6.iE 

I6.2E 

I6.3E 

i6.iE 

IS-7E 

I5-6E 

i6.iE 

Conn. 

Hartford 

S.iW 

S-6W 

6.iW 

6.8W 

7-SW 

8.2W 

8.7W 

9.4W 

9.8W 

I0.4W 

n.oW 

Del. 

Dover 

I.6W 

i.pW 

2.3W 

2.8W 

3-4W 

4-oW 

4-7W 

S-3W 

S-9W 

6.4W 

7-oW 

D.  C. 

Washington 

o.sE 

O.3E 

o.o 

o.sW 

LOW 

I.7W 

2.4W 

3-oW 

3.6W 

4.2W 

4-7W 

Fla. 

Jacksonville 

S.iE 

S.iE 

4-9E 

4.6E 

4.2E 

3-7E 

3-iE 

2.4E 

I.8E 

I.3E 

I.2E 

Pensacola 

7-7E 

7.8E 

7-7E 

7-SE 

7.2E 

6.8E 

6.2E 

S-6E 

S-oE 

4-SE 

4-4E 

Tampa 

6-4E 

6.2E 

5-9E 

5-SE 

S.oE 

4-SE 

3-9E 

3-3E 

2.8E 

2.3E 

2.0E 

Ga. 

Macon 

S.9E 

S-9E 

5-7E 

S-4E 

S.oE 

4-SE 

3-9E 

3.2E 

2.6E 

2.IE 

2.0E 

Haw. 

Honolulu 

_ 

_ 

_ 

_ 

94E 

9-4E 

9-SE 

9.8E 

10.  lE 

I0.4E 

io.6E 

Idaho 

Pocatello 

- 

- 

- 

- 

17.  4E 

I7-7E 

I7.8E 

17-  9E 

I7-7E 

I7-8E 

I8.4E 

Boise 

— 

_ 

— 

— 

iS.oE 

I8.4E 

I8.6E 

I8.7E 

I8.6E 

I8.8E 

I9-4E 

111. 

Bloomington 

6.3E 

6.5E 

6.6E 

6-sE 

6.3E 

S-9E 

S4E 

4-7  E 

4.IE 

3-6E 

3-4E 

Ind. 

Indianapolis 

S.oE 

S.IE 

S.oE 

4-7E 

4.4E 

3-8E 

3-2E 

2.6E 

2.0E 

i.4E 

i.iE 

la. 

Des  Moines 

_ 

IO.2E 

io.4E 

lO.sE 

I0.4E 

I0.2E 

9.7  E 

9.iE 

8.4E 

7-9E 

S.iE 

Kans. 

Emporia 

- 

- 

- 

- 

n.6E 

n.sE 

II.2E 

IO-7E 

10.  lE 

9-8E 

xo.iE 

Ness  City 

- 

- 

- 

- 

I2.4E 

I2.4E 

12.  2E 

H.9E 

II.4E 

u.iE 

ii-4E 

Ky. 

Lexington 

4-SE 

4-SE 

4.4E 

4.iE 

3-6E 

3-iE 

2.5E 

I.9E 

I.2E 

o.?E 

O.sE 

Princeton 

6.8E 

7-oE 

7.oE 

6.8E 

6.sE 

6.iE 

S.6E 

S.oE 

4-3E 

3-8E 

3-7E 

La. 

Alexandria 

8.4E 

8.?E 

8.8E 

8.8E 

8.?E 

8.4E 

S.oE 

7-4E 

6.9E 

6.6E 

6.8E 

Me. 

Eastport 

I3.6W 

I4-4W 

15.  2W 

i6.oW 

17.  oW 

I7.7W 

I8.2W 

I8.6W 

I8.7W 

19-oW 

I9-4W 

Portland 

p.oW 

9.6W 

io.3W 

n.oW 

n.6W 

I2.3W 

I2.8W 

I3-4W 

13-  9W 

I4-4W 

I4.8W 

Md. 

Baltimore 

o.pW 

i.iW 

I-4W 

i.gW 

2.4W 

3-iW 

3-8W 

4-4W 

S-oW 

S-6W 

6.iW 

Mass. 

Boston 

7-3W 

7.8W 

8.4W 

9-iW 

9-8W 

lo.sW 

n.oW 

n.SW 

I2.0W 

I2.6W 

13-  iW 

Mass. 

Pittsfield 

5-7W 

6.iW 

6.?W 

74W 

8.iW 

8.7W 

9-3W 

lO.oW 

I0.4W 

n.oW 

ii-SW 

Mich. 

Marquette 

- 

6.7  E 

6.?E 

6.sE 

6.oE 

S-4E 

4.6E 

3-8E 

3-oE 

2.3E 

2.0E 

Lansing 

- 

4.2E 

4.iE 

3-8E 

3-3E 

2.8E 

2.IE 

I.3E 

o.sE 

o.oE 

0.4E 

Minn. 

Northome 

— 

I0.4E 

I0.7E 

I0.8E 

I0.7E 

I0.4E 

lo.oE 

9-3E 

8.6E 

S.oE 

S.iE 

Mankato 

~ 

II.3E 

u.6E 

II.7E 

n.6E 

II.3E 

io.9E 

io.4E 

9-SE 

9.oE 

9.iE 

*  Tables  have  been  compiled  from  United  States  Magnetic  Tables  and  Magnetic  Charts  for  1905,  published  by 
the  Coast  and  Geodetic  Survey  in  1908. 
SMITHSONIAN  TABLES. 


TABLE  90  (continued). 

TERRESTRIAL   MAGNETISM  (continued}. 
Secular  Change  of  Declination  (continued). 


Ill 


State. 

Station. 

1810 

1820 

1830 

1840 

1850 

i860 

1870 

1880 

1890 

1900 

1910 

Miss. 

Jackson 

8.2E 

8-4E 

8.sE 

8.4E 

8.2E 

7-9E 

7-SE 

6.9E 

6.4E 

6.oE 

6.2E 

Mo. 

Sedalia 

- 

o.oE 

I0.2E 

I0.2E 

10.  lE 

9.8E 

94E 

8.7E 

8.oE 

7.6E 

7-9E 

Mont. 

Forsyth 

- 

- 

- 

I8.2E 

I8.SE 

I8.6E 

I8.6E 

I8.4E 

17.  9E 

17.  8E 

i8.3E 

Helena 

- 

- 

- 

I8.9E 

I9-3E 

I9-6E 

I9.8E 

I9.6E 

I9-4E 

I9-5E 

20.0E 

Nebr. 

Hastings 

— 

I.6E 

I2.0E 

I2.IE 

12.  lE 

I2.0E 

II.7E 

II.2E 

IO.SE 

I0.2E 

iQ-sE 

Nebr. 

Alliance 

_ 

- 

_ 

_ 

I5-4E 

IS-4E 

IS-3E 

I4.8E 

I4.3E 

I4.2E 

I4-SE 

Nev. 

Elko 

- 

- 

- 

- 

I7-3E 

I7.6E 

17.  7E 

I7-7E 

I7.6E 

17.  8E 

I8.3E 

Hawthorne 

- 

- 

- 

- 

I6-3E 

I6.6E 

I6.9E 

i7.oE 

i7.oE 

I7-3E 

I7.8E 

N.H. 

Hanover 

7.iW 

7-SW 

8.2W 

8.QW 

9.8W 

xo.sW 

ii.  iW 

n.6W 

I2.0W 

12.  sW 

13-oW 

N.J. 

Trenton 

2.8W 

3.iW 

3-SW 

4-lW 

4-7W 

S-4W 

6.oW 

6.?W 

7-2W 

7.8W 

8.4W 

N.  M. 

Santa  Rosa 

- 

- 

- 

- 

I2.7E 

I2.8E 

ia.7E 

I2.SE 

I2.lE 

I2.0E 

I2.4E 

Laguna 

— 

— 

— 

— 

13.  4E 

I3-6E 

I3-6E 

I3-4E 

13-  oE 

13-oE 

I3-SE 

N.Y. 

Albany 

S.6W 

S-8W 

6.3W 

6.9W 

7-6W 

8.4W 

9-iW 

9.8W 

I0.2W 

I0.8W 

n.4W 

Elmira 

2.2W 

2.4W 

2.8W 

3-3W 

4-oW 

4.8W 

S-4W 

6.3W 

7.oW 

7-6W 

8.iW 

N.  C. 

Newbern 

i.7E 

I.6E 

I.3E 

0.8E 

o.sE 

0.3W 

i.oW 

I.6W 

2.2W 

2.8W 

3.3W 

N.  C. 

Salisbury 

3-9E 

3-8E 

3-6E 

3.2E 

2.7E 

2.IE 

l.SE 

o.8E 

0.2E 

o.4W 

o.?W 

N.  Dak. 

Jamestown 

- 

- 

- 

- 

I4-5E 

I4-3E 

14-oE 

I3-5E 

i2.?E 

I2-4E 

I2.8E 

Dickinson 

— 

— 

— 

— 

i?.6E 

17  -6E 

I7-4E 

i?.oE 

I6-4E 

I6.2E 

I6.6E 

Ohio 

Columbus 

34E 

34E 

3.2E 

2.pE 

2.4E 

I.8E 

I.2E 

o.6E 

o.o 

o.?W 

i.iW 

Okla. 

Okmulgee 

~ 

~* 

~ 

~ 

I0.2E 

ro.iE 

9.8E 

9.4E 

8.8E 

8.SE 

8.9E 

Okla. 

Enid 

- 

- 

- 

- 

II.2E 

li.iE 

lO.gE 

IO.SE 

9-9E 

9-7E 

lO.iE 

Oreg. 

Sumpter 

— 

— 

— 

— 

I9-3E 

I9-7E 

2O.OE 

20.2E 

20.2E 

20.4E 

2I.OE 

Detroit 

i6.?E 

7-4E 

iS.oE 

I8.6E 

I9.2E 

I9-7E 

20.IE 

20.  4E 

20.sE 

20.8E 

2i.sE 

Pa. 

Philadelphia 

2.2W 

2.4W 

2.8W 

3-4W 

4.iW 

4.8W 

s-sw 

6.3W 

6.8W 

7-4W 

8.oW 

Altoona 

o.sW 

o.6W 

o.pW 

I.3W 

I.8W 

2.4W 

3.iW 

3.8W 

4-SW 

S-iW 

S.6W 

P.  R. 

San  Juan 

- 

- 

- 

_ 

_ 

_ 

_ 

_ 

_ 

i.oW 

2.0W 

R.I. 

Newport 

6.6W 

7.lW 

7.7W 

8.4W 

9-iW 

9.8W 

I0.3W 

io.8W 

II.3W 

n.9W 

I2.4W 

S.  C. 

Columbia 

4-4E 

4-3E 

4.iE 

3-7E 

3.2E 

2.7E 

2.IE 

i.4E 

O.SE 

0.2E 

o.iW 

S.D. 

Huron 

- 

- 

- 

13-iE 

13.  lE 

I2.9E 

I2.6E 

12.  lE 

n.4E 

ii.  lE 

n.4E 

Rapid  City 

— 

— 

— 

— 

i6.4E 

I6.4E 

I6.3E 

IS-8E 

IS-3E 

iS.iE 

I5-4E 

Tenn. 

Chattanooga 

S-3E 

S-3E 

S-iE 

4.8E 

4-4E 

3-9E 

3.3E 

2.6E 

2.0E 

l.SE 

I.3E 

Huntington 

- 

7-4E 

7-4E 

7-3E 

7.oE 

6.6E 

6.iE 

S-SE 

4-9E 

4-4E 

4-3E 

Tex. 

Houston 

— 

8.QE 

9.2E 

9-3E 

9-3E 

9.2E 

8.9E 

8.5E 

7-9E 

7-7E 

8.iE 

San  Antonio 

- 

- 

9.6E 

9.8E 

9-9E 

9.8E 

9-6E 

9-3E 

8.9E 

8.?E 

9.iE 

Pecos 

— 

— 

I0.8E 

n.oE 

li.iE 

ii.  lE 

n.oE 

I0.8E 

I0.4E 

io.3E 

io.?E 

Tex. 

Floydada 

_ 

- 

- 

_ 

H.3E 

II.3E 

II.2E 

lO.gE 

IO-4E 

I0.3E 

I0.7E 

Utah 

Salt  Lake 

- 

- 

- 

- 

I6-4E 

I6.6E 

i6.?E 

I6.SE 

I6.3E 

i6.sE 

I7.0E 

Vt. 

Rutland 

6.8W 

7-2W 

7.8W 

8.SW 

9-2W 

lO.oW 

I0.6W 

II.2W 

U.6W 

I2.IW 

I2.?W 

Va. 

Richmond 

0.8E 

0.6E 

0.3W 

o.iW 

0.6W 

I.2W 

I.8W 

2.sW 

3.iW 

3-7W 

4.2W 

Lynchburg 

i.9E 

I.8E 

I.6E 

I.2E 

0.8E 

O.2E 

o.sW 

I.2W 

I.8W 

2.4W 

2.8W 

Wash. 

Wilson  Creek 

2I.3E 

2I.6E 

2I.9E 

2I.9E 

22.IE 

22.4E 

22.9E 

Seattle 

19  lE 

I9-7E 

20.3E 

20.8E 

2I.3E 

2I.8E 

22.  lE 

22.3E 

22.6E 

23.oE 

23-SE 

W.  Va. 

Charleston 

2.3E 

2.2E 

2.0E 

I.6E 

i.iE 

O.sE 

0.2W 

0.9W 

i.SW 

2.IW 

2.6W 

Wis. 

Madison 

— 

8.6E 

8.?E 

8.6E 

8.3E 

7.8E 

7.2E 

6.4E 

S.6E 

S-qE 

4-9E 

Wyo. 

Douglas 

- 

- 

- 

- 

I5.8E 

i6.oE 

i6.oE 

IS-8E 

IS-4E 

IS-3E 

I5-7E 

Green  River 

I6.8E 

17-oE 

17.  oE 

I6.9E 

I6.6E 

I6.6E 

i?.oE 

SMITHSONIAN  TABLES. 


112  TABLES  91-92. 

TERRESTRIAL  MAGNETISM  (continued). 

TABLE  91.  — Dip  or  Inclination. 

This  table  gives  for  the  epoch  January  i,  1905,  the  values  of  the  magnetic  dip,  I,  corresponding 
to  the  longitudes  west  of  Greenwich  in  the  heading  and  the  north  latitudes  in  the  first  column. 


65° 

70° 

75° 

80° 

85° 

90° 

95° 

100° 

105° 

110° 

115° 

120° 

125° 

o 

o 

o 

0 

o 

o 

o 

o 

0 

0 

0 

0 

0 

0 

I9 

_ 

- 

48.8 

49.1 

47-5 

46.3 

44.8 

44-2 

43-9 

_ 

_ 

_ 

- 

21 

— 

— 

,51.0 

5" 

50.0 

49-3 

48.2 

47.0 

46.5 

— 

— 

— 

— 

23 
25 

_ 

_ 

560 

52.4 

51.8 

5°-7 
53-2 

49.6 
524 

48.8 

48.2 

50.6 

49-8 

48.3 

_ 

27 

- 

- 

58.9 

58.1 

57.6 

56-8 

55.6 

547 

53-9 

S3-1 

52.6 

S'-o 

- 

29 

31 

- 

60.7 

63.0 

61.0 
63.1 

60.2 
62.6 

59-8 
62.0 

58.9 
£.3 

58.2 
60.6 

57-2 

56.2 

S8.7 

55-5 
57-7 

54-8 
56-7 

56.0 

- 

33 

_ 

65.0 

65.0 

64.6 

64.0 

63.5 

62.7 

02  o 

61.0 

SQ-8 

S8.9 

S8.i 

_ 

35 

_ 

67.0 

66.9 

66.  s 

66.0 

6s.6 

64.9 

63.7 

62.7 

62.3 

61.0 

60.2 

_ 

37 

- 

68.6 

68.9 

68.6 

68.2 

67.7 

66.9 

66.2 

65.1 

64.6 

62.9 

62.2 

- 

39 

_ 

70.3 

70.6 

70.4 

70.2 

69.7 

68.8 

68.1 

67.2 

66.1 

65.0 

64.0 

62.8 

— 

71.8 

72.2 

72.2 

71.9 

71.4 

70.8 

69.8 

68.9 

67.8 

66.8 

65.6 

64.7 

43 
45 
47 

74-4 
75-7 

73-5 
74.8 
76.2 

73-9 
75-6 
76.9 

74.1 

73-8 
75-4 
76.9 

73-3 
75-° 
76.8 

72.6 

74-3 
76.0 

71.6 
73-6 

75-2 

70.7 
72.4 
74-2 

69.6 
71-5 
73-o 

68.6 
70-3 
71.8 

67-5 
69.2 
70.8 

66.3 

68.1 
69.9 

49 

76.8 

78.1 

78.2 

78.3 

78.7 

78.1 

77-5 

76.8 

75-8 

74-5 

73-5 

72.3 

71.4 

TABLE  92. -Secular  Change  of  Dip. 

Values  of  magnetic  dip  for  places  designated  by  the  north  latitudes  and  longitudes  west  of 
Greenwich  in  the  first  two  columns  for  January  ist  of  the  years  in  the  heading.  The  degrees 
are  given  in  the  third  column  and  minutes  in  the  succeeding  columns. 


Lati- 
tude. 

Longi- 
tude. 

i8S5 

i860 

1865 

1870 

1875 

1880 

1885 

I800 

I89S 

1900 

I90S 

1910 

0 

o 

0 

f 

, 

r 

, 

, 

, 

f 

, 

, 

, 

, 

, 

25 

80 

55+ 

49 

49 

48 

46 

43 

40 

35 

35 

39 

48 

60 

77 

25 

no 

49+ 

08 

20 

3° 

39 

46 

55 

61 

68 

76 

86 

96 

1  06 

30 
30 

83 

100 

60+ 
57+ 

66 

44 

70 

49 

74 
67 

73 
70 

65 

I 

51 
61 

63 
77 

78 
90 

96 

I05 

30 

"5 

54+ 

53 

62 

69 

7i 

70 

72 

75 

79 

85 

96 

101 

35 

80 

66+ 

57 

58 

57 

54 

45 

35 

26 

21 

20 

22 

3° 

38 

35 

90 

£5t 

65 

59 

44 

37 

32 

26 

25 

25 

27 

36 

48 

35 

I05 

62+ 

— 

— 

32 

3° 

24 

24 

24 

29 

34 

42 

5° 

35 

120 

60+ 

°3 

06 

08 

08 

07 

06 

08 

II 

13 

14 

12 

08 

40 

75 

7M 

- 

82 

82 

78 

73 

65 

55 

43 

33 

27 

24 

24 

24 

40 

90 

70+ 

30 

31 

34 

37 

36 

32 

29 

26 

25 

26 

3° 

36 

40 
40 

105 

120 

67+ 
64+ 

48 

4~6 

56 
44 

53 

51 
44 

51 
44 

44 

52 
45 

56 

60 

48 

3 

45 

65 

74+ 

116 

no 

101 

92 

So 

68 

57 

46 

35 

28 

24 

20 

45 

75 

75+ 

103 

99 

95 

90 

85 

73 

62 

53 

43 

38 

36 

34 

45 

90 

74- 

81 

81 

81 

79 

77 

75 

68 

63 

61 

59 

60 

60 

45 

I05 

72- 

— 

— 

— 

— 

— 

22 

20 

20 

21 

22 

24 

27 

45 

122.5 

68- 

35 

34 

37 

40 

40 

39 

37 

34 

3° 

26 

24 

20 

49 

92 

78- 

26 

25 

24 

22 

20 

20 

15 

12 

II 

09 

06 

04 

49 

120 

72H 

26 

24 

22 

22 

19 

20 

19 

19 

19 

18 

16 

SMITHSONIAN  TABLES. 


TABLES  93-94. 

TERRESTRIAL   MAGNETISM  (continued). 

TABLE  93.  — Horizontal  Intensity. 

This  table  gives  for  the  epoch  January  i,  1905,  the  horizontal  intensity,  H,  expressed  in  C.G.  S. 
units,  corresponding  to  the  longitudes  in  the  heading  and  the  latitudes  in  the  first  column. 


65° 

70° 

75° 

80° 

85° 

90° 

95° 

100° 

105° 

110° 

115° 

120° 

125° 

o 

19 

_ 

_ 

.307 

.3M 

•319 

.322 

.328 

.332 

•331 

21 

- 

- 

.301 

•309 

.314 

•310 

.320 

.324 

•324 

23 

— 

— 

.293 

•3°3 

•3°5 

•309 

.312 

•315 

•317 

.320 

2S 

— 

— 

.284 

.292 

.304 

•3°7 

.308 

.309 

.312 

•304 

27 

— 

— 

.274 

.280 

.286 

.289 

.296 

.298 

.300 

•303 

•306 

.298 

29 

_ 

•257 

.262 

.269 

.276 

.281 

.286 

.289 

.292 

.294 

.297 

.291 

31 

- 

.246 

.251 

.256 

.263 

.269 

.274 

.277 

.282 

.284 

.285 

.282 

33 

— 

•233 

•239 

•245 

.251 

•257 

.262 

.266 

.270 

•273 

.274 

.274 

35 

— 

.220 

•22.S 

.232 

.240 

.242 

.248 

•2  53 

.256 

•259 

.262 

.265 

37 

- 

.208 

.209 

.218 

.222 

.226 

.232 

.238 

•245 

.246 

.252 

.251 

39 
4i 

- 

.184 

.198 

.i8S 

.203 
.186 

.206 
.192 

.212 
.196 

.217 
.202 

.224 
.207 

.229 
.216 

.237 
.223 

.240 
.228 

.242 

.240 

31 

43 

— 

.170 

.170 

.169 

•!75 

.178 

.187 

.194 

.201 

.210 

.215 

.222 

.226 

4,S 

.161 

•157 

•155 

.156 

•157 

.162 

.169 

.177 

.190 

.192 

.208 

.215 

47 

•145 

.144 

.140 

.142 

.142 

.150 

.152 

.161 

.170 

.ISO 

.188 

.IQ6 

.201 

49 

•131 

.129 

•I25 

.126 

.124 

.129 

.138 

.146 

•'53 

.165 

•175 

.182 

.187 

TABLE  94.  —Secular  Change  of  Horizontal  Intensity. 

Values  of  horizontal  intensity  in  C.  G.  S.  units  for  places  designated  by  the  latitude  and  longi- 
tude in  the  first  two  columns  for  January  i  of  the  years  in  the  heading. 


Latitude.  1 

ii 

1855 

1860 

1865 

1870 

1875 

1880 

1885 

1890 

I89S 

1900 

1905 

1910 

0 

o 

25 

80 

•3°99 

.3086 

•3073 

•3057 

.3042 

•3025 

.3008 

.2990 

.2970 

.2949 

.2920 

.2890 

25 
30 

no 

83 

.3229 
.2803 

.3218 
•2795 

.3204 
.2788 

.3189 
.2780 

•3  '70 

.2772 

.3155 
.2763 

•3H3 
•2752 

•3130 
.2740 

•3"7 

.2725 

.3104 
.2706 

ielo 

•3°75 
.2644 

30 

100 

— 

.2961 

.2942 

.2924 

.2907 

.2891 

.2877 

.2865 

.2850 

.2830 

.2804 

30 

"5 

.3040 

.3026 

.3011 

.2996 

.2979 

.2964 

.2952 

.2940 

.2929 

.2920 

.2910 

.2898 

35 

80 

.2384 

•2379 

•2374 

.2369 

.2367 

•2363 

•2359 

•2352 

•2347 

•2337 

.2320 

.2296 

35 

90 

— 

.2462 

.2462 

.2461 

.2458 

•2455 

.2447 

•2437 

.2430 

•2399 

35 
35 

105 

120 

: 

: 

: 

.2720 

.2620 
.2707 

.2608 
.2695 

•2599 
.2683 

.2590 
.2672 

.2583 

•2573 
.2656 

.2560 
.2650 

•2544 
.2644 

40 

75 

.1880 

.1883 

.1891 

.1902 

.1911 

.1919 

.1925 

.1930 

•i93i 

.1928 

.1920 

.1909 

40 

90 

_ 

.2086 

.2082 

.2079 

.2076 

.2075 

.2074 

.2072 

.2068 

.2060 

.2050 

.2036 

40 

105 

— 

— 

— 

.2272 

.2266 

.2261 

.2257 

•2253 

.2248 

.2240 

.2230 

.2217 

40 

120 

— 

— 

— 

.2429 

.2420 

.2412 

.2406 

.2392 

.2386 

.2380 

•2379 

45 
45 

65 

75 

.1504 
.1483 

•I5M 
.1485 

.1525 
.1488 

•I537 
•'495 

.1506 

.1567 
.1516 

.1578 
•1527 

:I5538 

.1600 
.1546 

•1550 

.1610 
•1550 

.1610 
•1554 

45 

90 

_ 

•1635 

•1633 

.1631 

.1628 

.1626 

.1624 

.1623 

.1624 

.1623 

.1620 

.1616 

45 

105 

— 

.1920 

.1919 

.1918 

.1916 

•1913 

.1910 

.1906 

.1900 

.1892 

AS 

122.5 

.2175 

.2170 

.2162 

•2153 

.2145 

•2135 

.2127 

.2121 

.2117 

.2115 

.2115 

.2115 

*49 

49 

92 

120 

.1332 
.1841 

•1330 
.1841 

.1328 
.1840 

.1324 
.1839 

.1321 
.1836 

•1319 
.1831 

.1318 
.1826 

.I3l8 
.1821 

.1819 

.1324 
.1820 

•1330 
.1820 

•1335 
.1824 

SMITHSONIAN  TABLES. 


TABLES  95-96. 
TERRESTRIAL  MAGNETISM   (continued). 

TABLE  95.  —  Total  Intensity. 

This  table  gives  for  the  epoch  January  i,  1905,  the  values  of  total  intensity,  F,  expressed  in  C.  G.  S. 
units  corresponding  to  the  longitudes  in  the  heading  and  the  latitudes  in  the  first  column. 


65° 

70° 

75° 

80° 

858 

90° 

95° 

100° 

105° 

110° 

HS° 

120° 

125° 

0 

_ 

.466 

.480 

.472 

.466 

.462 

•463 

•459 

j 

21 

_ 

- 

478 

.492 

.489 

485 

.480 

•475 

•471 

_ 

_ 

_ 

_ 

23 

- 

- 

•495 

•5°4 

.500 

.500 

•493 

.486 

.481 

.480 

- 

- 

- 

25 

- 

- 

.512 

.522 

.514 

•5^5 

•507 

•503 

•495 

•487 

•483 

•457 

- 

27 

*• 

•~ 

•530 

•530 

•534 

.528 

•524 

.516 

•509 

•505 

.504 

•474 

— 

29 
31 

_ 

•525 
•542 

•540 

•541 
•556 

•549 
.560 

•544 
.560 

-.ill 

•534 
•547 

•525 
•543 

•519 
•53i 

•515 
•519 

.492 

•5°4 

- 

33 

- 

•551 

.566 

•57  l 

•572 

•s£ 

.571 

.567 

•543 

•530 

.518 

- 

35 

— 

•5^3 

•574 

.582 

•590 

.586 

.584 

•571 

•558 

•557 

•540 

•533 

— 

37 

- 

•570 

.581 

•598 

.598 

.596 

•591 

•590 

.582 

•573 

•553 

•538 

- 

39 

j 

•584 

.596 

.605 

.608 

.611 

.600 

.600 

•591 

•585 

.568 

.552 

•536 

- 

•589 

.605 

.608 

.618 

.614 

.614 

.600 

.600 

•579 

c8i 

43 
45 
47 

•599 
•587 

•599 

.613 
.623 
.618 

.617 
.623 
.622 

.627 
.623 
.626 

.619 
.626 

.657 

.625 
.624 
.628 

.614 
.627 
.630 

.608 
.628 
.624 

!6o5 
.616 

-589 
.590 
.602 

.580 
.586 
•596 

1? 

49 

•574 

^626 

.611 

.621 

•633 

.626 

.638 

•639 

.624 

617 

.616 

•599 

'Isl 

TABLE  96. -Secular  Change  of  Total  Intensity. 

Values  of  total  intensity  in  C.  G.  S.  units  for  places  designated  by  the  latitudes  and  longitudes  in  the 
first  two  columns  for  January  i  of  the  years  in  the  heading.    (Computed  from  Tables  92  and  94.) 


Lati- 
tude. 

Longi- 
tude. 

1855 

1860 

1865 

1870 

1875 

1880 

1885 

1890 

1895 

1900 

1905 

1910 

0 

25 

o 
80 

•5516 

•5493 

•5467 

•5434 

.5400 

•5364 

•5322 

.5290 

.5264 

•5247 

.5222 

.5206 

25 

110 

4938 

•4933 

•4925 

.4908 

.4902 

.4891 

.4883 

.4876 

•4873 

.4868 

.4860 

3° 

83 

.5800 

.5796 

.5790 

•5777 

•5757 

.5720 

.5668 

•5625 

.5600 

•5590 

.558i 

•5559 

30 
30 

100 

115 

•5285 

.5280 

.5583 
.5269 

•5570 
•5247 

•5544 
•5215 

•5499 
•5194 

•5456 
•5179 

•5432 
•5167 

.5427 
.5160 

•5421 
•5i58 

.5416 
W 

•5405 
.5140 

35 

80 

.6089 

.6080 

.6063 

.6038 

•5996 

•5946 

.5900 

.5863 

.5874 

.5830 

.5818 

•5789 

35 

90 

— 

— 

— 

•5991 

•5964 

•5942 

.5912 

.5901 

.5882 

•5865 

.58<8 

•5852 

35 

105 

- 

- 

- 

•5674 

.5629 

.5610 

•5590 

•5588 

•5585 

•5582 

•5572 

35 
40 

1  20 

75 

.6206 

.6216 

6220 

.5462 
.6227 

•5433 

.0212 

.5406 
.6182 

IS 

•5374 
.6098 

•536i 
.6070 

•535° 
.6045 

•5332 
.6019 

•5399 
•5985 

40 
40 

90 

105 

: 

.6254 

.6258 

.6264 
.6048 

.6250 
.6019 

.6226 

•5997 

.6208 

.5986 

.6187 
•5976 

.6170 
.5967 

.6151 
•5963 

.6141 

•5953 

•6i35 
•5940 

40 
45 
45 

120 
65 

75 

.6188 
•6454 

.6186 
.6431 

.6167 
.6413 

.5691 
.6152 
.6404 

.5670 
.6134 
.6412 

•5651 
.6107 

•6363 

•5637 
.6077 
.6327 

.5620 
.6048 
.6306 

.5608 
.6019 
.6266 

•5593 
.6005 
.6247 

•5590 
•5987 
•6233 

•5591 
.5962 
.6235 

45 
45 

90 

i°5 

- 

.6465 

•6457 

•6434 

.6408 

.6386 
•6332 

.6330 
.6314 

.6291 
.6303 

.6382 
.6299 

.6264 
.6392 

.6284 

.6244 
.627; 

45 

122.5 

•5956 

.5938 

.5930 

.5918 

.5896 

.5864 

•5834 

.5804 

•5776 

•5754 

•5745 

•5728 

49 
49 

92 

120 

.6643 

.6624 
.6100 

!6o8s 

.6566 
.6071 

ss? 

•6523 
.6028 

.6472 
.6017 

•5995 

.6451 
.5988 

.6447 
•5992 

•6430 
•5986 

.6456 
•5988 

SMITHSONIAN  TABLES. 


TABLE  97. 
AGONIC  LINE. 

The  line  of  no  declination  appears  to  be  still  mov. 
ing  westward  in  the  United  States,  but  the  line  of  no 
annual  change  is  only  a  short  distance  to  the  west  of 
it,  so  that  it  is  probable  that  the  extreme  westerly 
position  will  soon  be  reached. 


Lat 

N. 

Longitudes  of  the  agonic  line  for  the  years  — 

1800 

1850 

i875 

1890 

'90S 

0 

o 

o 

o 

o 

o 

25 

- 

- 

- 

75.5 

76.1 

30 

— 

- 

— 

78.0 

797 

35 

6 

7-2 

76.7 
77-3 

79.0 

B? 

81.7 
82.8 

7 

76^3 

777 

806 

82.2 

83*5 

8 
9 

76.7 
76.9 

78.3 
78.7 

81.3 
81.6 

82.6 
82.2 

83.6 

40 

77-0 

79-3 

81.6 

82.7 

84.0 

i 

77-9 

80.4 

81.8 

82.8 

84.6 

2 

79.1 

81.0 

82.6 

837 

84.8 

3 
4 

79-8 

81.2 

83.1 
83-3 

84-3 
84.9 

85.0 
85.5 

45 

« 

_  , 

83.6 

85.2 

86.0 

6 

— 

_ 

84.2 

84.8 

86.4 

7 

- 

- 

85.1 

85.4 

86.4 

8 

— 

— 

86.0 

86.5 

9 

" 

86.5 

86.3 

87.2 

SMITHSONIAN  TABLE*. 


TABLE  98. 


PRESSURE   OF   COLUMNS   OF   MERCURY  AND  WATER. 

British  and  metric  measures.    Correct  at  o°  C.  for  mercury  and  at  4°  C.  for  water. 


METRIC  MEASURE. 

BRITISH  MEASURE. 

Cms.  of 
Hg. 

Pressure 
in  grammes  per 

sq.  cm. 

Pressure 
in  pounds  per 
sq.  inch. 

Inches  of 
Hg. 

Pressure 
in  grammes  per 
sq.  cm. 

Pressure 
in  pounds  per 
sq.  inch. 

1 

I3-S956 

0.193376 

1 

34-533 

0.491174 

2 

27.1912 

0.386752 

2 

69.066 

0.982348 

3 

40.7868 

0.580128 

3 

103.598 

1.473522 

4 

54-3824 

0773504 

4 

138-131 

1.964696 

5 

67.9780 

0.966880 

5 

172.664 

2.455870 

6 

81-5736 

1.160256 

6 

207.197 

2.947044 

7 

95.1692 

I-353632 

7 

241.730 

3438218 

8 

108.7648 

1.547008 

8 

276.262 

3.929392 

9 

122.3604 

1.740384 

9 

310.795 

4.420566 

10 

I35-9560 

1.933760 

10 

345-328 

4.911740 

Cms.  of 
H2O. 

Pressure 
in  grammes  per 
sq.  cm. 

Pressure 
in  pounds  per 
sq.  inch. 

Inches  of 
H2O. 

Pressure 
in  grammes  per 
sq.  cm. 

Pressure 
in  pounds  per 
sq.  inch. 

1 

I 

0.0142234 

1 

2.54 

0.036127 

2 

2 

0.0284468 

2 

5.08 

0.072255 

3 

3 

0.0426702 

3 

7-62 

0.108382 

4 

4 

0.0568936 

4 

10.16 

0.144510 

5 

5 

O.07III70 

5 

12.70 

0.180637 

6 

6 

0.0853404 

6 

15.24 

0.216764 

7 

7 

0.0995638 

7 

17.78 

0.252892 

8 

8 

0.1137872 

8 

20.32 

0.289019 

9 

9 

O.I280I06 

9 

22.86 

0.325M7 

10 

10 

0.1422340 

10 

25.40 

0.361274 

SMITHSONIAN  TABLES. 


._,..      TABLE  99.  117 

REDUCTION  OF  BAROMETRIC  HEICHT  TO  STANDARD   TEMPERATURE.* 


Corrections  for  brass  scale  and 
English  measure. 

Corrections  for  brass  scale  and 
metric  measure. 

Corrections  for  glass  scale  and 
metric  measure. 

Height  of 
barometer  in 
inches. 

a 

in  inches  for 
temp.  F. 

Height  of 
barometer  in 
mm. 

a 

in  mm.  for 
temp.  C. 

Height  of 
barometer  in 
mm. 

a 
in  mm.  for 
temp.  C. 

15.0 

0.00135 

400 

0.0651 

50 

0.0086 

16.0 

.00145 

410 

.0668 

100 

.0172 

17.0 

.00154 

420 

.0684 

I5° 

.0258 

17-5 

.00158 

430 

.0700 

200 

•°345 

18.0 

.00163 

440 

.0716 

250 

.0431 

18.5 

.00167 

450 

.0732 

300 

•0517 

19.0 

.00172 

460 

.0749 

350 

.0603 

19-5 

.00176 

470 

.0765 

480 

.0781 

400 

0.0689 

20.0 

0.00181 

490 

.0797 

450 

.0775 

20.5 

.00185 

500 

.0861 

21.0 

.00190 

500 

0.0813 

520 

.0898 

21-5 

.00194 

5*0 

.0830 

540 

•0934 

22.0 

.00199 

520 

.0846 

560 

.0971 

22.5 

.00203 

53° 

.0862 

580 

.1007 

23.0 

.00208 

540 

.0878 

23-S 

.00212 

.0894 

600 

0.1034 

560 

.0911 

610 

.1051 

24.0 

O.002I7 

570 

.0927 

620 

.1068 

24-5 

.00221 

580 

•0943 

630 

.1085 

25.0 

.00226 

590 

•0959 

640 

.1103 

25-5 
26.0 

.OO23I 
.00236 

600 

0.0975 

650 
660 

.1120 
-"37 

26.5 

.00240 

610 

.0992 

27.0 

.00245 

620 

.1008 

670 

0.1  1  54 

27.5 

.OO249 

630 

.1024 

680 

.1172 

640 

.1040 

690 

.1189 

28.0 

O.O0254 

650 

.1056 

700 

.1206 

28.5 

.00258 

660 

.1073 

710 

.1223 

29.0 

.00263 

670 

.1089 

720 

.1240 

29.2 

.00265 

680 

.1105 

730 

.1258 

29.4 

.00267 

690 

.1121 

29.6 

.OO268 

740 

0.1275 

29.8 
30.0 

.OO27O 
.00272 

700 

710 

O.II37 

•"54 

& 

.1292 
.1309 

720 

.1170 

770 

.1327 

30.2 

O.00274 

730 

.1186 

780 

•1344 

304 

.00276 

740 

.1202 

790 

.1361 

30.6 

.00277 

.1218 

800 

.1378 

30.8 

.00279 

760 

"•1235 

31.0 
31.2 

.00281 
.00283 

780 

.1267 

850 

900 

0.1464 

31.4 

.00285 

790 

.1283 

95° 

.1639 

31.6 

.00287 

800 

.1299 

1000 

.1723 

*The  height  of  the  barometer  is  affected  by  the  relative  thermal  expansion  of  the  mercury  and 
the  glass,  in  the  case  of  instruments  graduated  on  the  glass  tube,  and  by  the  relative  expansion  of 
the  mercury  and  the  metallic  inclosing  case,  usually  of  brass,  in  the  case  of  instruments  graduated 


numbers  tabulated  under  a  are  the  values  of  a  in  the  equation  Ht  =  Hf  —  a  (tf  —  /)  where  Iff  is  the 
height  at  the  standard  temperature,  Hf  the  observed  height  at  the  temperature  f,  and  a  (/'  —  t)  the 
correction  for  temperature.  The  standard  temperature  is  o°  C.  for  the  metric  system  and  28°.s  F. 
for  the  English  system.  The  English  barometer  is  correct  for  the  temperature  of  melting  ice  at  a 
temperature  of  approximately  28°.5  F.,  because  of  the  fact  that  the  brass  scale  is  graduated  so  as 
to  be  standard  at  62°  F.,  while  mercury  has  the  standard  density  at  32°  F. 

EXAMPLE.— A  barometer  having  a  brass  scale  gave  H—  765  mm.  at  25°  C. ;  required,  the  cor- 
responding reading  at  o°  C.  Here  the  value  of  a  is  the  mean  of  .1235  and  .1251,  or.  1243; .  •.  a  (t'—t) 
—  .1243  X  25  =  3.11.  Hence  HO  =  765  —  3.11  =  761.89. 

N.  B. — Although  a  is  here  given  to  three  and  sometimes  to  four  significant  figures,  it  is  seldom 
worth  while  to  use  more  than  the  nearest  two-figure  number.  In  fact,  all  barometers  have  not  the 
same  values  for  a,  and  when  great  accuracy  is  wanted  the  proper  coefficients  have  to  be  deter- 
mined by  experiment. 

SMITHSONIAN  TABLES. 


TABLE  1OO. 


CORRECTION   OF   BAROMETER   TO  STANDARD   GRAVITY, 


Height 
above  sea 
level  in 
metres. 

Observed  height  of  barometer  in  millimetres. 

15000 
14500 
14000 
13500 
13000 
12500 

12000 
II500 
I  IOOO 
10500 
IOOOO 

9500 

9000 
8500 
8000 
7500 

7000 
6500 
6000 

5500 
5000 
4500 

4000 

3500 
3000 

2500 

2OOO 
1500 
IOOO 
500 

400 

450 

500 

«o 

600 

6S0 

700 

750 

800 

100 
2OO 
300 
400 

700 
800 
900 
IOOO 
1  100 
1200 
1300 
1400 
1500 
IOOO 
1700    , 
I800 
1900 
2OOO 
2100 
22OO 
2300 
2400 
2500 
26OO 
2700 
2800 
2900 
3000 
3100 
32OO 
3300 
3400 
3500 
3600 
3700 
3800 
3900 
4000 

C< 

tres 
sea 
and 
in  to 

•195 
•203 
•211 
.219 
.227 
•235 
•243 

.291 
.299 
.307 
•3H 

nrectiot 
for  ele 
level  in 
height 

p  line. 

.176 
.185 
.194 
.203 
.212 
.220 
.229 
.238 
•247 

I 

.292 
.201 
•309 

in  mi 
vation 
first  cc 
of  baro 

.147 

•if 

[216 
.226 
•236 
•245 
.255 
.265 

•275 
.285 
.294 

lime- 
above 
lumn 
meter 

.108 
.118 
.129 
.140 

.172 
•183 
.194 

.204 

•259 
.270 

.118 
.130 
.142 

•'53 
.165 
.176 
.188 

.200 
.212 

.224 
•235 
•247 
•259 
.271 
•283 
•295 

.064 
.077 
.000 
.103 

.141 

SB 

.179 
.191 
.204 
.217 
.230 
.242 
•255 

.014 
.028 
.041 

;o82 
.096 
.109 
.123 

•137 
.150 
.164 
.178 
.191 
.205 

•015 
.030 
.044 
-059 
•073 
.088 
.102 
.117 
.131 
.146 

.Ol6 
.032 
.047 
.063 
.078 

-245 
.203 
.162 
.120 
.088 
.046 
.004 
.962 
.920 
.879 
•837 

•795 
•753 

edths 
above 
i  and 
ottom 

•340 
.292 

•244 
.106 
.149 
.101 

1-053 
1.005 

•957 
•9°9 
.861 
.813 
.765 

in  hundi 
•levation 
st  columr 
icter  in  b 

1-345 
1.291 

1-237 
1.184 
1.130 
1.076 
i.  022 
.969 

-915 
.861 
.807 

•753 
.700 

rections 
inch  for  ( 
;vel  in  la 
t  of  baron 

1.255 
I.I96 
I.I36 
1.076 

i.  oi  6 

•957 
.897 

.837 
•777 
.718 
.658 
.598 

Coi 
of  an 
sea  1 
heigh 
line. 

1.077 
1.005 

.790 
.718 
.646 
•574 
•503 
•431 

;2i5 

1.0  JO 

.918 

.8^3 
.787 
.721 

$ 

.724 
.658 
•592 
.526 
.461 

•395 

•779 
.701 
.623 

•545 
.467 

•389 
•3" 
•233 

.078 

•503 
419 

•335 
.251 
.167 
.084 

.192 
.096 

.179 
.090 

32 

30 

28 

26 

r>4 

22 

20 

18 

16 

M 

Height 
above  sea 
level  in 
feet. 

Observed  height  of  barometer  in  inches. 

SMITHSONIAN  TABLES. 


TABLE  101. 

REDUCTION   OF   BAROMETER   TO   STANDARD   GRAVITY.* 

Redaction  to  Latitude  45°.— English.  Scale. 

N.  B.     From  latitude  o°  to  44°  the  correction  is  to  be  subtracted. 
From  latitude  90°  to  46°  the  correction  is  to  be  added. 


119 


Latitude. 

Height  of  the  barometer  in  inches. 

*9 

20 

21 

22 

23 

24 

25 

26 

27 

28 

29 

30 

Inch. 

Inch. 

Inch. 

Inch. 

Inch. 

Inch. 

Inch. 

Inch. 

Inch. 

Inch. 

Inch. 

Inch. 

0° 

90° 

0.051 

0.053 

0.056 

0.059 

0.061 

0.064 

0.067 

0.069 

0.072 

0.074 

0.077 

0.080 

5 

85 

0.050 

0.052 

0.055 

0.058 

0.060 

0.063 

0.066 

0.068 

0.071 

0.073 

0.076 

0.079 

6 

84 

.049 

.052 

•055 

•057 

.060 

.062 

.065 

.068 

.070 

•073 

.076 

.078 

7 

83 

.049 

.052 

.054 

•057 

•059 

.062 

.065 

.067 

.070 

.072 

.075 

.077 

8 

82 

.049 

.051 

•054 

.056 

.059 

.061 

.064 

.067 

.069 

.072 

.074 

.077 

9 

81 

.048 

.051 

•053 

.056 

.058 

.061 

.063 

.066 

.068 

.071 

•073 

.076 

10 

80 

0.048 

0.050 

0-053 

0-055 

0.058 

O.o6o 

0.063 

0.065 

0.068 

0.070 

0.073 

0.075 

ii 

79 

.047 

.049 

.052 

•054 

•057 

.059 

.062 

.064 

.067 

.069 

.072 

.074 

12 

78 

.046 

.049 

.051 

•054 

.056 

.058 

.061 

.063 

.066 

.068 

.071 

•073 

13 

77 

•045 

.048 

•050 

•053 

•055 

•057 

.060 

.062 

.065 

.067 

.069 

.072 

H 

76 

•045 

.047 

.049 

.052 

•054 

.056 

.059 

.061 

•063 

.066 

.068 

.071 

15 

75 

0.044 

0.046 

0.048 

0.051 

0-053 

0.055 

0.058 

0.060 

0.062 

O.o6  C 

0.067 

0.069 

16 

74 

•043 

•045 

.047 

.050 

.052 

.054 

.056 

•059 

.061 

.063 

.065 

.068 

17 

73 

.042 

.044 

.046 

.049 

.051 

•053 

•055 

•057 

.060 

.062 

.064 

.066 

18 

72 

.041 

•043 

•045 

.047 

.050 

.052 

•054 

.056 

.058 

.060 

.062 

.065 

J9 

7i 

.040 

.042 

*044 

.046 

.048 

.050 

.052 

•055 

•057 

•°59 

.061 

.063 

20 

70 

0.039 

0.041 

0.043 

0.045 

0.047 

0.049 

0.051 

0-053 

0.055 

0.057 

0.059 

0.061 

21 

69 

.038 

.040 

.042 

.044 

•045 

.047 

.049 

.051 

.053 

•055 

•057 

•°59 

22 

68 

.036 

.038 

.040 

.042 

.044 

.046 

.048 

.050 

.052 

•054 

.056 

•057 

23 

67 

•035 

•037 

•039 

.041 

•043 

.044 

.046 

.048 

.050 

.052 

•054 

•055 

24 

66 

•034 

.036 

•037 

•039 

.041 

•043 

•045 

.046 

.048 

.050 

.052 

•053 

25 

65 

0.033 

0.034 

0.036 

0.038 

0.039 

0.041 

0.043 

0.044 

0.046 

0.048 

0.050 

0.051 

26 

64 

.031 

•°33 

•034 

.036 

.038 

.039 

.041 

•043 

.044 

.046 

.048 

.049 

27 

63 

.030 

.031 

•033 

.034 

.036 

.038 

•039 

.041 

.042 

.044 

•045 

.047 

28 

62 

.028 

.030 

.031 

•033 

•034 

.036 

•037 

•039 

.040 

.042 

•043 

•045 

29 

61 

.027 

.028 

.030 

.031 

.032 

•034 

•035 

•037 

.038 

•039 

.041 

.042 

30 

60 

0.025 

0.027 

0.028 

0.029 

0.031 

0.032 

0.033 

0.035 

0.036 

0-037 

0.039 

0.040 

31 

59 

.024 

.025 

.026 

.027 

.029 

.030 

.031 

.032 

.034 

•035 

.036 

•037 

32 

58 

.022 

.023 

.025 

.026 

.027 

.028 

.029 

.030 

.032 

•033 

•034 

•°35 

33 

57 

.O2I 

.022 

.023 

.024 

.025 

.026 

.027 

.028 

.029 

.030 

.031 

.032 

34 

56 

.019 

.020 

.021 

.022 

.023 

.024 

.025 

.026 

.027 

.028 

.029 

.030 

35 

55 

0.017 

0.018 

0.019 

0.020 

O.O2I 

O.O22 

O.O23 

0.024 

O.O25 

0.025 

0.026 

0.027 

36 

54 

.016 

.016 

.017 

.018 

.019 

.020 

.O2I 

.021 

.022 

.023 

.024 

.025 

53 

.014 

.015 

.015 

.016 

.017 

.018 

.018 

.019 

.020 

.O2I 

.021 

.022 

38 

52 

.OI2 

.013 

.014 

.014 

.015 

.015 

.016 

.017 

.017 

.018 

.019 

.OI9 

39 

5i 

.Oil 

.Oil 

.012 

.012 

.013 

.013 

.014 

.014 

.015 

.015 

.Ol6 

.017 

40 

50 

O.OO9 

0.009 

O.OIO 

O.OIO 

0.0  1  1 

0.0  1  1 

0.012 

0.012 

0.012 

0.013 

0.013 

0.014 

4i 

49 

.007 

.007 

.008 

.008 

.009 

.009 

.009 

.OIO 

.OIO 

.OIO 

.Oil 

.Oil 

42 

48 

.005 

.006 

.006 

.006 

.006 

.007 

.007 

.007 

.008 

.008 

.008 

.008 

43 

47 

,004 

.004 

.004 

.004 

.004 

.004 

.005 

.005 

•005 

.005 

.005 

.OO6 

44 

46 

.OO2 

.002 

.002 

.002 

.002 

.002 

.002 

.002 

•003 

.003 

.003 

.003 

*  "  Smithsonian  Meteorological  Tables,"  p.  58. 


SMITHSONIAN  TABLES. 


I2O  TABLE  102. 

REDUCTION   OF   BAROMETER   TO  STANDARD  GRAVITY, 

Reduction  to  Latitude  45°.—  Metric  Scale. 

N.  B.  —  From  latitude  o°  to  44°  the  correction  is  to  be  subtracted. 
From  latitude  90°  to  46°  the  correction  is  to  be  added. 


Latitude. 

Height  of  the  barometer  in  millimetres. 

520 

560 

600 

620 

640 

660 

680 

700 

720 

740 

760 

780 

mm. 

mm. 

mm. 

mm. 

mm. 

mm. 

mm. 

mm. 

mm. 

mm. 

mm. 

mm* 

0° 

90° 

1.38 

1.49 

1.  60 

I.6S 

1.70 

1.76 

1.81 

1.86 

1.92 

1.97 

2.02 

2.08 

5 

85 

.36 

1.47 

!-57 

1.63 

1.68 

i-73 

1.81 

1.84 

i.89 

1.94 

1-99 

2.04 

6 

84 

•35 

I.46 

1.56 

1.61 

1.67 

1.72 

1.78 

1.82 

1.87 

I  98 

2.03 

7 

83 

•34 

i-45 

J-55 

i.  60 

1.65 

1.70 

1.77 

1.81 

1.86 

1.01 

1.0 

2.OI 

8 

82 

•33 

1-43 

i-54 

I-59 

1.64 

1.69 

1.76 

1.79 

1.84 

1.89 

1.94 

2.OO 

9 

81 

•32 

1.42 

1.52 

1.62 

1.67 

1.74 

1.77 

1.82 

1.87 

1.92 

I.97 

10 

80 

•3° 

1.40 

1.50 

!.ss 

1.  60 

1.65 

1.70 

i-75 

1.80 

I.8C 

1.90 

i-95 

ii 

79 

.28 

1.38 

1.48 

1.53 

1.58 

1.63 

1.68 

1.78 

1.83 

1.88 

'•93 

12 

78 

.26 

1-36 

1.46 

«•$] 

1.56 

i.  60 

1.65 

1.70 

•75 

1.80 

1.85 

1.90 

'3 

77 

.24 

1.44 

1.48 

1.53 

1.58 

1.63 

1.67 

.72 

1.77 

1.82 

1.87 

76 

.22 

1.32 

1.41 

1.46 

1.50 

i-55 

i.  60 

1.65 

.69 

1.74 

1.79 

1.83 

15 

75 

.20 

1.29 

1-38 

i-43 

1.48 

1.52 

J-57 

1.61 

.66 

1.71 

T-75 

1.80 

16 

74 

•17 

1.26 

1.40 

1.44 

1.49 

i-54 

•58 

•63 

1.67 

1.72 

1.76 

17 

73 

1.24 

1.32 

i-37 

1.41 

i-45 

1.50 

•54 

•59 

1-63 

1.68 

1.72 

18 

72 

.12 

1.  21 

1.29 

i-34 

1.38 

1.42 

1.46 

•55 

1.64 

1.68 

19 

1.09 

I.I7 

1.26 

1.30 

i-34 

1.38 

i-43 

•47 

!-55 

1.64 

20 

70 

1.  06 

I.I4 

1.22 

1.26 

1.31 

1.35 

i-39 

.43 

•47 

1.51 

i-55 

i-59 

21 

69 

1.03 

I.  II 

I.I9 

1.23 

1.27 

I-3I 

.38 

.42 

1.46 

1.50 

i-54 

22 

68 

1.  00 

1.07 

1.19 

1.26 

1.30 

•34 

•38 

1.42 

1.46 

1.49 

23 

67 

0.96 

1.04 

I.  II 

«$ 

1.18 

1.22 

1.26 

.29 

•33 

i-37 

1.41 

1.44 

24 

66 

•93 

1.  00 

1.07 

I.IO 

1.14 

1.18 

1.  21 

•25 

.28 

1.32 

i-35 

J-39 

25 

65 

0.89 

0.96 

1.03 

1.06 

I.IO 

i.!3 

1.16 

.20 

.23 

1.27 

1.30 

i-33 

26 

64 

.85 

.92 

0.98 

i.  02 

1.05 

1.08 

i.  ii 

•15 

.18 

1.  21 

1.25 

1.28 

27 

63 

.81 

.88 

•94 

0.97 

I.OO 

1.03 

i.  06 

.IO 

•13 

1.16 

1.19 

1.22 

28 

62 

•77 

•83 

.89 

.92 

0.95 

0.98 

I.OI 

.04 

1.07 

I.IO 

1.16 

29 

61 

•73 

•79 

•85 

.87 

.90 

•93 

0.96 

0.99 

1.02 

1.04 

1.07 

I.IO 

30 

60 

0.69 

0-75 

0.80 

0.83 

0.85 

0.88 

0.91 

0.94 

0.96 

0.98 

I.OI 

1.04 

31 

59 

.65 

.70 

•75 

•77 

.80 

.82 

•85 

.87 

.90 

.92 

°-95 

0.97 

32 

58 

.61 

•65 

.70 

•72 

•75 

•77 

•79 

.82 

.84 

.86 

.89 

.91 

33 

57 

.56 

.61 

.65 

.67 

.69 

•74 

.76 

.78 

.80 

.82 

.84 

34 

56 

•52 

.56 

.60 

.62 

.64 

'.66 

.68 

.70 

.72 

•74 

.76 

.78 

35 

55 

0.47 

0.51 

o-55 

0.56 

0.58 

0.60 

0.62 

0.64 

0.66 

0.67 

0.69 

0.71 

36 

54 

•43 

.46 

•49 

•51 

•53 

•54 

.56 

•58 

•59 

.61 

•63 

.64 

37> 

53 

.38 

.41 

•44 

•45 

•47 

.48 

•50 

•51 

•53 

•54 

.56 

•57 

38 

52 

•33 

.36 

•39 

.40 

.41 

•43 

.44 

•45 

.46 

.48 

•49 

•50 

39 

51 

.29 

•31 

•33 

•34 

•35 

•37 

•38 

•39 

.40 

.41 

.42 

•43 

40 

50 

0.24 

0.26 

0.28 

0.29 

0.30 

0.31 

0.31 

0.32 

o-33 

0-34 

0.35 

0.36 

41 

49 

.19 

.21 

.22 

•23 

.24 

.24 

•25 

.26 

•27 

•27 

.28 

.29 

42 

48 

.14 

.16 

•17 

•17 

.18 

.18 

.19 

.19 

.20 

.21 

.21 

.22 

43 
44 

8 

.10 
•05 

.10 

•05 

.11 

.06 

.12 
.06 

.12 
.06 

.12 
.06 

3 

•13 

.07 

•13 

.07 

.14 

.07 

.14 

.07 

.14, 
.07 

Smithsonian  Meteorological  Tables,"  p.  59. 


SMITHSONIAN  TABLES. 


TABLE  103.  121 

CORRECTION  OF  THE  BAROMETER  FOR  CAPILLARITY.* 


i.  METRIC  MEASURE. 

HEIGHT  OF  MENISCUS  IN  MILLIMETRES. 

Diameter 
of  tube 

0.4 

0.6 

0.8 

1.0 

1.2 

1.4 

1.6 

1.8 

in  mm. 

Correction  to  be  added  in  millimetres. 

4 

I 

0.83 

•47 
.27 

1.22 

0.65 
.41 

o'.86 
.56 

1.98 
1.19 
0.78 

2-37 
0.98 

1.80 

I.2I 

1-43 

- 

7 

.18 

.28 

.40 

.67 

0.82 

0.97 

I-I3 

8 

- 

.20 

.29 

.38 

.46 

.56 

•65 

0.77 

9 

— 

.15 

.21 

.28 

•33 

.40 

.46 

•52 

10 

— 

— 

•15 

.20 

•25 

.29 

•33 

•37 

ii 

— 

— 

.IO 

.14 

.18 

.21 

.24 

•27 

12 

- 

- 

.07 

.10 

•13 

•15 

.18 

.19 

13 

.04 

.07 

.10 

.12 

•13 

.14 

2.  BRITISH  MEASURE. 

HEIGHT  OF  MENISCUS  IN  INCHES. 

Diameter 
of  tube 

.01 

.02 

.03 

.04 

.05 

.06 

.07 

.08 

in  inches. 

Correction  to  be  added  in  hundredths  of  an  inch. 

•15 
.20 

I.IO 

4.70 

2.2O 

6.86 
3-28 

9-23 

4-54 

11.56 
5-94 

7.85 

- 

- 

•25 

•3° 

0-55 
•36 

1.20 
0.79 

1.92 
1.26 

2.76 
1.77 

3-68 
2.30 

4.72 
2.88 

5.88 
348 

4.20 

•35 
.40 

•51 
.40 

0.82 
.61 

a8i 

1.49 

1.02 

1.85 

1.22 

2.24 
1.42 

2.65 
1.62 

•45 
•5° 

— 

•32 

.20 

•35 

0.68 
•47 

0.83 
•56 

0.96 
.64 

1.15 
0.71 

•55 

.08 

.20 

•3i 

.40 

•47 

•52 

*  The  first  table  is  from  Kohlrausch  (Experimental  Physics),  and  is  based  on  the  experiments  of  Mendelejeff  and 
Gutkowski  (Jour,  de  Phys.  Chem.  Geo.  Petersburg,  1877,  or  Wied.  Beib.  1867).  The  second  table  has  been  calcu- 
lated from  the  same  data  by  conversion  into  inches  and  graphic  interpolation. 

A  number  of  tables,  mostly  based  on  theoretical  formulae  and  the  capillary  constants  of  mercury  in  glass  tubes  in 
air  and  vacuum,  were  given  in  the  fourth  edition  of  Guyot's  Tables,  and  may  be  there  referred  to.  They  are  not 
repeated  here,  as  the  above  is  probably  more  accurate,  and  historical  matter  is  excluded  for  convenience  in  the  use 
of  the  book. 

SMITHSONIAN  TABLES. 


122 


TABLE  104. 


AERODYNAMICS. 


The  pressure  on  a  plane  surface  normal  to  the  wind  is  for  ordinary  wind  velocities  expressed  by 


where  k  is  a  constant  depending  on  the  units  employed,  w  the  mass  of  unit  volume  of  the  air, 
a  the  area  of  the  surface  and  v  the  velocity  of  the  wind.*  Engineers  generally  use  the  table  of 
values  of  P  given  by  Smeaton  in  1759.  This  table  was  calculated  from  the  formula 

P=.  00492  v2 

and  gives  the  pressure  in  pounds  per  square  foot  when  v  is  expressed  in  miles  per  hour.  The 
corresponding  formula  when  v  is  expressed  in  feet  per  second  is 

^=.00228^. 

Later  determinations  do  not  agree  well  together,  but  give  on  the  average  somewhat  lower 
values  for  the  coefficient.  The  value  of  w  depends,  of  course,  on  the  temperature  and  the  baro- 
metric pressure.  Langley's  experiments  give  kw  =  .  00166  at  ordinary  barometric  pressure  and 
10°  C.  temperature. 

For  planes  inclined  at  an  angle  a  less  than  90°  to  the  direction  of  the  wind  the  pressure  may 
be  expressed  as  />a=^aAo- 

Table  104,  founded  on  the  experiments  of  Langley,  gives  the  value  of  F*  for  different  values  of 
a.  The  word  aspect,  in  the  headings,  is  used  by  him  to  define  the  position  of  the  plane  relative  to 
the  direction  of  motion.  The  numerical  value  of  the  aspect  is  the  ratio  of  the  linear  dimension 
transverse  to  the  direction  of  motion  to  the  linear  dimension,  a  vertical  plane  through  which  is 
parallel  to  the  direction  of  motion. 


TABLE  104. -Values  ol  Fa  In  Equation  Pa=TaP9 


Plane  30  in.  X  4.8  in. 
Aspect  6  (nearly). 

Plane  12  in.  X  12  in. 
Aspect  i. 

Plane  6  in.  X  24  in. 
Aspect  \. 

a 

Fa. 

a 

*; 

a 

fa 

0° 

0.00 

0° 

0.00 

0° 

0.00 

5 

0.28 

5 

0.15 

5 

0.07 

10 

0.44 

10 

0.30 

10 

0.17 

IS 

°-55 

15 

0.44 

15 

0.29 

20 

0.62 

20 

0.57 

20 

0.43 

25 

0.66 

25 

0.69 

25 

0.58 

3° 

0.69 

30 

0.78 

30 

0.71 

35 

0.72 

35 

0.84 

- 

- 

40 

0.74 

40 

0.88 

— 

— 

45 

0.76 

45 

0.91 

- 

- 

50 

0.78 

50 

- 

- 

- 

*  The  following  pressures  in  pounds  per  square  inch  show  roughly  the  influence  of  the  shape  and  size  of  the  resist- 
ing surface  (Dines'  results).    The  wind  velocity  was  20.9  miles  per  hour.    The  flat  plates  were  f  in.  thick. 


Square,  sides  4  in 1.51 

Circle,  same  area 51 

Rectangle,  16  in.  by  i 70 

Square,  12  in.  sides 57 

Circle,  same  area , 55 

Rectangle,  24  in.  by  6 .59 

Square,  sides  16  in 52 

Plate,  6  in.  diam.  4!  thick 1.45 

Ditto,  curved  side  to  wind  . 0.92 

Sphere,  6  in.  diam 0.67 

SMITHSONIAN  TABLES. 


Plate,  6  in.  diam.  90°  cone  at  back    ......  1.49 

Same,  cone  in  front     ...........  0.98 

'      sharp  30°  cone  at  back    ........  i  .54 

"      cone  in  front      ...........  0.60 

5  in.  Robinson  cup  on  8J  in.  of  J  in.  rod    ....  1.68 

Same,  with  back  to  wind  .........     .  0.73 

9  in.  cup  on  6£  in.  of  f  in.  rod 
Same,  with  back  to  wind 


1.75 
,  0.60 


2j  in.  cup  on  gj  in.  of^i  in.  rod     .......    a.6o 

Same,  with  back  to  wind     ...»    .....    1.04 


TABLE  105. 


123 


AERODYNAMICS. 

On  the  basis  of  the  results  given  in  Table  104  Langley  states  the  following  condition  for  the 
soaring  of  an  aeroplane  76.2  centimetres  long  and  12.2  centimetres  broad,  weighing  500  grammes, 
—  that  is,  a  plane  one  square  foot  in  area,  weighing  i.i  pounds.  It  is  supposed  to  soar  in  a 
horizontal  direction,  with  aspect  6. 

TABLE  106.  -  Data  for  the  Soaring  of  Planes  76.2  X  12.2  cms.  weighing  600  Grammes,  Aspect  6. 


Weight  of  planes  of  like 

Inclination 

Soaring  speed  v. 

Work  expended  per  minute 
(activity). 

form,  capable  of  soaring 
at  speed  v  with  the  ex- 
penditure of  one  horse 

to  the  hori- 

power. 

zontal  a. 

Metres  per 
sec. 

Feet  per 
sec. 

Kilogramme 
metres. 

Foot 
pounds. 

Kilogrammes. 

Pounds. 

2° 

20.0 

66 

24 

174 

95-0 

209 

5 
10 

15 

15.2 
I2.4 
11.2 

50 
41 
37 

I 

297 

474 
623 

55-5 

34-8 
26.5 

122 

^ 

30 

45 

10.6 

II.  2 

35 
37 

'3 

1268 
2434 

13.0 
6.8 

29 
IS 

In  general,  if  p= 

Soaring  speed  z>=  y  £ .-^J- 
Activity  per  unit  of  weight =v  tan  a 

The  following  data  for  curved  surfaces  are  due  to  Wellner  (Zeits.  fur  Luftschifffahrt,  x.,  Oct. 

1893)- 

Let  the  surface  be  so  curved  that  its  intersection  with  a  vertical  plane  parallel  to  the  line  of 
motion  is  a  parabola  whose  height  is  about  -^  the  subtending  chord,  and  let  the  surface  be 
bounded  by  an  elliptic  outline  symmetrical  with  the  line  of  motion.  Also,  let  the  angle  of  incli- 
nation of  the  chord  of  the  surface  be  a,  and  the  angle  between  the  direction  of  resultant  air 
pressure  and  the  normal  to  the  direction  of  motion  be  0.  Then  j8  <  a,  and  the  soaring  speed  is 

v=  A  £ l- — ,  while  the  activity  per  unit  of  weight  =z/tan  ft. 

\  k  Fa.  cos  ft 
The  following  series  of  values  were  obtained  from  experiments  on  moving  trains  and  in  the 

wind. 

Angle  of  inclination  a  =  —3°  o°  +3°  6°  9°  12° 

Inclination  factor  Fa=  0.20  0.50  0.75  0.90  i.oo  1.05 

tan£=  o.o  i  0.02  0.03  0.04  o.io  0.17 

Thus  a  curved  surface  shows  finite  soaring  speeds  when  the  angle  of  inclination  a  is  zero  or  even 
slightly  negative.    Above  a  =  12°  curved  surfaces  rapidly  lose  any  advantage  they  may  have  for 
small  inclinations. 
SMITHSONIAN  TABLES. 


I24 


TABLE  106. 


FRICTION. 

The  following  table  of  coefficients  of  friction/  and  its  reciprocal  i/f,  together  with  the  angle  of  friction  or  angle  of 
repose  <£,  is  quoted  from  Rankine's  "Applied  Mechanics."  It  was  compiled  by  Rankine  from  the  results  of 
General  Morin  and  other  authorities,  and  is  sufficient  for  all  ordinary  purposes. 


Material. 

/ 

I// 


* 

Wood  on  wood,  dry       
"      "      "       soaov  . 

.25--50 
.20 

4.00-2.00 

r  QO 

14.0-26.5 

II.  C 

yvv 

2  OO—  I  67 

-3 

26.5—31.0 

"      "    wet        
"        "      "    soaov     , 

.24-.  26 
.20 

4-I7-3-85 
c.OO 

13-5-14-5 

II.  < 

"        "    elm  dry         

C.OO-4..OO 

1  1.  5—14.0 

Hemp  on  oak,  dry         
«        «      «    Wet         

•53 
.Tl 

1.89 
3.OO 

28.0 
i8.«; 

7  7O—  2  86 

I  C  O—  IQ  C 

"        "   metals,  dry  
«        «        "       wet  

'•$ 

1.79 
2.78 

i^.ij—  iy.^ 

29-5 
2O.O 

"        «        «       greasy 

.27 

4.-5C 

I-J.Q 

"        "        "        oily         

•IS 

6.67 

6.67—5.00 

835 
8.c-ii.e 

"       "        "       wet  

,* 

•3    T-7 

16.1; 

Smooth  surfaces,  occasionally  greased  . 
"        continually  greased  . 
*'           "        best  results        .... 
Steel  on  agate,  dry  *      
"      «      «       oiled*  

.O7~.o8 

•°5 
•03-.036 
.20 
.107 

I4.3-I2.50 

20.00 
33-3-27-6 
5-00 
O.^C 

4.0-4.5 
3-o 
1.75-2.0 

"•$ 

6.1 

Iron  on  stone         
Wood  on  stone      
Masonry  and  brick  work,  dry        .... 
"         '•      "        "       damp  mortar 
"       on  dry  clay      

•30-70 
About  .40 
.60-70 
74 

•Si 
.-i  -i 

3-33-1-43 
2.50 
1.67-1.43 

III 

3.00 

16.7-35.0 

22.0 

33-o-35-o 
36-5 
27.0 

lS.2< 

Earth  on  earth       
"       "       "     dry  sand,  clay,  and  mixed  earth  . 
«       "       «      damp  clay    

.25-1.00 
•38-75 

I.OO 

4.00-1.00 
2-63-1  -33 

I.OO 

14.0-45.0 
21.0-37.0 
4C.O 

"       "       "      wet  clay        
"       "       a     shingle  and  gravel 

.81-1.  n 

3-23 
1.23-0.9 

17.0 
39.0-48.0 

*  Quoted  from  a  paper  by  Jenkin  and  Ewing,  "  Phil.  Trans.  R.  S."  vol.  167.  In  this  paper  it  is  shown  that  in 
cases  where  "  static  friction  "  exceeds  "  kinetic  friction  "  there  is  a  gradual  increase  of  the  coefficient  of  friction  as  the 
speed  is  reduced  towards  zero. 

SMITHSONIAN  TABLES. 


TABLE  107. 
VISCOSITY. 


125 


The  coefficient  of  viscosity  is  the  tangential  force  per  unit  area  of  one  face  of  a  plate  of  the 
fluid  which  is  required  to  keep  up  unit  distortion  between  the  faces.  Viscosity  is  thus  measured 
in  terms  of  the  temporary  rigidity  which  it  gives  to  the  fluid.  Solids  may  be  included  in  this 
definition  when  only  that  part  of  the  rigidity  which  is  due  to  varying  distortion  is  considered. 
One  of  the  most  satisfactory  methods  of  measuring  the  viscosity  of  fluids  is  by  the  observation  of 
the  rate  of  flow  of  the  fluid  through  a  capillary  tube,  the  length  of  which  is  great  in  comparison 
with  its  diameter.  Poiseuille  *  gave  the  following  formula  for  calculating  the  viscosity  coefficient 

in  this  case :  /i  =  *      s,  where  h  is  the  pressure  height,  r  the  radius  of  the  tube,  s  the  density  of 

the  fluid,  v  the  quantity  flowing  per  unit  time,  and  /  the  length  of  the  capillary  part  of  the  tube. 
The  liquid  is  supposed  to  flow  from  an  upper  to  a  lower  reservoir  joined  by  the  tube,  hence  h 
and  /  are  different.  The  product  hs  is  the  pressure  under  which  the  flow  takes  place.  Hagen- 
bach  t  pointed  out  that  this  formula  is  in  error  if  the  velocity  of  flow  is  sensible,  and  suggested  a 
correction  which  was  used  in  the  calculation  of  his  results.  The  amount  to  be  subtracted  from 

v2 
A,  according  to  Hagenbach,  is    i-     ,  where  g  is  the  acceleration  due  to  gravity.    Gartenmeister  \ 

points  out  an  error  in  this  to  which  his  attention  had  been  called  by  Finkener,  and  states  that  the 
quantity  to  be  subtracted  from  h  should  be  simply  — ;  and  this  formula  is  used  in  the  reduction 

of  his  observations.  Gartenmeister's  formula  is  the  most  accurate,  but  all  of  them  nearly  agree 
if  the  tube  be  long  enough  to  make  the  rate  of  flow  very  small.  None  of  the  formulae  take  into 
account  irregularities  in  the  distortion  of  the  fluid  near  the  ends  of  the  tube,  but  this  is  probably 
negligible  in  all  cases  here  quoted  from,  although  it  probably  renders  the  results  obtained  by  the 
"  viscosimeter  "  commonly  used  for  testing  oils  useless  for  our  purpose. 

The  term  "  specific  viscosity "  is  sometimes  used  in  the  headings  of  the  tables ;  it  means  the 
ratio  of  the  viscosity  of  the  fluid  under  consideration  to  the  viscosity  of  water  at  a  specified  tem- 
perature. 

The  friction  of  a  fluid  is  proportional  to  the  size  of  the  rubbing  surface,  to  -33  where  v  is  the 

velocity  of  motion  in  a  direction  perpendicular  to  the  rubbing  surface,  and  to  a  constant  known 
as  the  viscosity. 

Variation  of  Viscosity  of  Water,  with  Temperature.   Dynes  per  s<j.  cm. 


Temp. 

Poise  ville. 
1846. 

Sprung. 
1876. 

Slotte. 
1883. 

Thorpe-Rogers. 

Specific 
viscosity. 

c. 

Slotte. 
1883. 

Thorpe-Rogers. 
1894- 

Specific 
Viscosity. 

0° 

5 

0.01716 

0.01778 
.01510 

0.01808 
.01524 

0.01778 
.01510 

1.  000 
.849 

If 

0.00510 
.00472 

0.00506 
.00468 

.285 
•263 

10 

15 

.01309 
.01146 

.01301 
•OH35 

.01314 
.01144 

•01303 
.01134 

a 

65 

70 

.00438 
.00408 

.00436 
.00406 

.245 
.228 

20 

.01008 

.01003 

.01008 

.01002 

.564 

75 

.00382 

.00380 

.214 

25 

.00897 

.00896 

.00896 

.00891 

.501 

80 

.00358 

.00356 

.200 

30 

.00803 

.00802 

.00803 

.00798 

.449 

85 

•00337 

.00335 

.188 

35 

.00721 

.00723 

.00724 

.OO72O 

.405 

90 

.00318 

.00316 

•178 

40 

.00653 

.00657 

.00657 

.00654 

.368 

95 

.00301 

.00299 

.168 

45 

•00595 

.00602 

.00602 

.00597 

.336 

100 

.00285 

.00283 

•159 

50 

•00553 

•00553 

.00548 

*3 

*  "  Comptes  rendus,"  vol.  15,  1842 ;  "  M6m.  Serv»  l£tr."  1846. 

t  "  Pogg.  Ann."  vol.  109,  1860. 

t  "  Zeitschr.  Phys.  Chem."  vol.  6,  1890. 

§  Thorpe  and  Rogers,  "  Philos.  Trans."  i8sA,  1894;  "  Proc.  Roy.  Soc."  55, 1894. 


SMITHSONIAN  TABLES. 


126 


TABLES  108-110. 

VISCOSITY. 

TABLE  108. -Solution  of  Alcohol  in  Water.* 

Coefficients  of  viscosity,  in  C.  G.  S.  units,  for  solution  of  alcohol  in  water. 


Temp. 

Percentage  by  weight  of  alcohol  in  the  mixture. 

o 

8.21 

16.60 

34.58 

43-99 

53-36 

75-75 

87.45 

99.73 

0° 

O.OlSl 

0.0287 

0.0453 

0.0732 

0.0707 

0.0632 

0.0407 

0.0294 

O.OlSo 

5 
10 

.0152 
.0131 

.0234 
.0195 

.0351 
.0281 

•0558 

•0435 

•°552 
.0438 

.0502 
.0405 

•0344 
.0292 

.0256 
.0223 

.0163 
.0148 

15 

20 

.0114 
.0101 

.0165 
.0142 

.0230 
.0193 

•0347 
.0283 

•0333 
.0286 

.0332 
.0276 

.0250 
.0215 

.0195 
•0172 

.0134 
.0122 

25 

30 

0.0090 
.008I 

0.0123 
.OI08 

0.0163 
.0141 

0.0234 
.0196 

0.0241 
.0204 

O.O232 
.0198 

0.0187 
.0163 

O.OI52 

O.OIIO 
.0100 

35 

.0073 

.0096 

.OI22 

.0167 

.0174 

.0171 

.0144 

.OI2O 

.0092 

40 

.0067 

.0086 

.0108 

.0143 

.0150 

.0149 

.0127 

.0107 

.0084 

45 

.0061 

.0077 

.0095 

.0125 

.0131 

.0130 

.0113 

.0097 

.0077 

50 

0.0056 

O.OO7O 

0.0085 

0.0109 

0.0115 

O.OII5 

0.0102 

0.0088 

O.OO7O 

55 

.0052 

.0063 

.0076 

.0096 

.0102 

.OIO2 

.0091 

.0086 

.0065 

60 

.0048 

.0058 

.0069 

.0086 

.0091 

.O092 

.0083 

.0073 

.0000 

The  following  tables  (152-153)  contain  the  results  of  a  number  of  experiments  in  the  viscosity  of  mineral  oils  derived 
from  petroleum  residues  and  used  for  lubricating  purposes.! 


TABLE  109. -Mineral  Oila.t 


1 

If. 

11 

5* 

It 

Sp.  viscosity.    Water  at 

20°  C.  =  I. 

1 

°C. 

°C. 

20°  C. 

50°  C. 

100°  C. 

•931 

243 

274 

_ 

11.30 

2.9 

.921 
.906 

216 
189 

246 
208 

- 

7.31 
345 

2-5 

i-5 

.921 

163 

190 

- 

27.80 

2.8 

.917 

132 

168 

- 

- 

2.6 

.904 
.891 

170 
i  Si 

207 
182 

8.65 
4-77 

2.65 
1.86 

1.7 

I-3 

.878 

108 

148 

2.94 

1.48 

.855 

42 

45 

1.65 

- 

•90S 

I65 

202 

_ 

3.10 

I-S 

.894 

139 

270 

7.60 

3.60 

i-3 

.866 

90 

224 

2.50 

1.50 

TABLE  110. -Oils. 


on. 

A 
f 
] 

3* 

P 

°c. 

0  Burning  [I 
P  point. 

Viscosity  at  1 
19°  C.,  water 
ati9°C.=i.  1 

Cylinder  oil  .    . 
Machine  oil  .    . 

.917 
.914 

227 
213 

274 
260 

IQI 

IO2 

Wagon  oil     .    . 

.914 

148 

182 

80 

«<        <( 
Naphtha  residue 

.911 
.910 

157 
134 

I87 
162 

70 

55 

Oleo-naphtha     . 

.910 

219 

2S7 

121 

(i               a 

.904 

2OI 

242 

66 

u              u 

.894 

184 

222 

26 

Oleonid     .    .    . 

.884 

I8.S 

2I7 

28 

best 

quality 

.881 

1  88 

224 

20 

Olive  oil   .    .    . 

.916 

_ 

_ 

22 

Whale  oil      .    . 

.879 

_ 

_ 

o. 

«       «« 

•875 

" 

8 

*>This  table  was  calculated  from  the  table  of  fluidities  given  by  Noack  (Wied.  Ann.  vol.  27,  p.  217),  and  shows  a 
maximum  for  a  solution  containing  about  40  per  cent  of  alcohol.  A  similar  result  was  obtained  for  solutions  of  acetic 
acid. 

t  Table  152  is  from  a  paper  by  Engler  in  Dingler's  "  Poly.  Jour."  vol.  268,  p.  76,  and  Table  153  is  from  a  paper  by 
Lamansky  in  the  same  journal,  vol.  248,  p.  29.  The  very  mixed  composition  of  these  oils  renders  the  viscosity  a  very 
uncertain  quantity,  neither  the  density  nor  the  flashing  point  being  a  good  guide  to  viscosity. 

%  The  different  groups  in  this  table  are  from  different  residues. 

SMITHSONIAN  TABLES. 


TABLE  111. 
VISCOSITY. 


I27 


This  table  gives  some  miscellaneous  data  as  to  the  viscosity  of  liquids,  mostly  referring  to  oils  and  paraffins.    The 

viscosities  are  in  C.  G.  S.  units. 


Liquid. 

G.% 

Coefficient 
of 
viscosity. 

Temp. 
Cent.  ° 

Authority. 

0.0160 

II.Q 

Poiseuille. 

M 

O.OI49 

J.  A.y 
14-5 

4 

Anisol  ...... 

O.OI  1  1 

2O.O 

Gartenrneister. 

42.20 

2.8 

Schottner. 

S\+i*4i\J 

25.18 

8.1 

M 

M 

n  87 

14  1 

« 

« 

x    ' 
8  10 

•"•'f-J 
2O  *? 

U 

« 

U.JV 

A  QA 

^U.j 

26.1; 

U 

Glycerine  and  water    . 

9446 

t'^rr 

7-437 

•W»J 

8-5 

<« 

<»                   « 

80.31 

i.  02  1 

8-5 

«< 

«                   « 

64.05 

0.222 

8.5 

« 

«                   « 

49-79 

0.092 

8.5 

M 

Glycol          

O.02I9 

0.0 

Arrhenius. 

O.Ol84 

—  20 

Koch. 

0.0170 

0.0 

«( 

. 

0.0157 

20.0 

M 

... 

0.0122 

100.0 

<( 

... 

O.OI  O2 

2OO.O 

«« 

. 

0.0093 

300.0 

• 

0.1878 

20.O 

Gartenmeister* 

Olive  oil       

0.9890 

15.0 

Brodmann. 

Paraffins:  Decane 

0.0077 

22.3 

Bartolli  &  Stracciati. 

Dodecane  . 

0.0126 

23-3 

«                 «« 

Heptane 

O.OO45 

24.0 

«                 « 

Hexadecane 

0.0359 

22.2 

««                 «< 

Hexane 

0.0033 

23-7 

«                 « 

Nonane       .        »        . 

0.0062 

22.3 

<«                 « 

Octane 

0.0053 

22.2 

«                 « 

Pentane 

O.OO26 

21.0 

«                                M 

Pentadecane 

0.0281 

22.0 

<«                                « 

Tetradecane 

0.0213 

21.9 

«(                                «( 

Tridecane  .        .        . 

0.0155 

23-3 

«                                <i 

Undecane   .        . 

00095 

22.7 

«                     a 

Petroleum  (Caucasian) 

O.OI90 

17-5 

Petroff. 

Rape  oil       ..... 

2C.T 

o.o 

O.  E.  Meyer. 

«     «< 

DO 

3-»S 

1  0.0 

« 

"     " 

1.63 

2O.O 

«< 

(i          U 

0.96 

30.0 

« 

*  Calculated  from  the  £ormuh/*  =  .oi7~.oooo6^/+oooooo2i^--x)oooooooo2S/3  (vide  Koch,  Wied.  Ann.  vol.  14. 


SMITHSONIAN  TABLES. 


128 


TABLE  112. 
VISCOSITY. 


This  table  gives  the  viscosity  of  a  number  of  liquids  together  with  their  temperature  variation. 
The  headings  are  temperatures  in  Centigrade  degrees,  and  the  numbers  under  them  the  coeffi- 
cients of  viscosity  in  C.  G.  S.  units.* 


Temperature  Centigrade. 

1 

0° 

10° 

20° 

30° 

40° 

50° 

70° 

90° 

jj 

Acetates:  Methyl 

_ 

.0046 

.0041 

.0036 

.0032 

.0030 

_ 

_ 

Ethyl 

— 

.0051 

.0044 

.0040 

•0035 

.0032 

_ 

— 

Propyl 

— 

.0066 

.0059 

.0052 

.0044 

•0039 

_ 

— 

Allyl 

_ 

.0068 

.006l 

.0054 

.0049 

.0044 

_ 

_ 

Amyl 

- 

.OIO6 

.0089 

.0077 

.0065 

.0058 

_ 

. 

Acids  :  Formic 

— 

.02262 

.Ol8O4 

.01465 

.01224 

.01025 

_ 

•. 

2 

Acetic 

— 

.0150 

.0126 

.0109 

.0094 

.0082 

_ 

_ 

I 

Propionic 

- 

.0125 

.0107 

.0092 

.008I 

.0073 

- 

- 

3 

" 

— 

.0139 

.0118 

.OIOI 

.0091 

.0080 

— 

— 

i 

Butyric 

- 

.0196 

.0163 

.0136 

.0118 

.OIO2 

'       - 

- 

2 

Valeric 

— 

.0271 

.O22O 

.0183 

.OI55 

.0127 

— 

— 

3 

Salicylic 

— 

.0320 

.O27I 

.O222 

.Ol8l 

.0150 

— 

_ 

3 

Alcohol  :  Methyl 

.00813 

.00686 

.00591 

.00515 

.00450 

.00396 

- 

- 

4 

Ethyl 

.01770 

.01449 

.01192 

.00990 

.00828 

.00698 

.00504 

— 

4 

Propyl 

.03882 

.02917 

.02255 

.01778 

.01403 

.01128 

•00757 

.00526 

4 

Butyric 

•05185 

.03872 

.02947 

.02266 

.01780 

.01409 

.00926 

.00633 

4 

Allyl 

.02144 

.01703 

.OI36l 

.01165 

.00911 

.00760 

.00548 

.00407 

4 

Isopropyl 

.04564 

•03245 

.02369 

•OI755 

.01329 

.OIO26 

.00642 

— 

4 

Isobutyl 
Amyl  (op.-inac.) 

.08038 
•08532 

•05547 
.06000 

.03906 
.04341 

.02863 
.03206 

.O2I2I 
.02414 

.01609 
.01849 

.00973 
.01147 

•00633 
.00758 

4 

4 

Aldehyde 

.00267 

.00244 

.OO222 

— 

— 

— 

— 

— 

3 

Aniline 

— 

.0440 

.0319 

.0241 

.0189 

— 

_ 

5 

Benzole 

.00902 

.00759 

.00649 

.00562 

.00492 

.00437 

•00351 

- 

4 

Bromides  :  Ethyl 

.00478 

.00432 

.00392 

•00357 

— 

— 

4 

Propyl 

.00645 

•00575 

•00517 

.00467 

.00425 

.00388 

.00328 

- 

4 

Allyl 

.00619 

•00552 

.00496 

.00449 

.00410 

.00374 

.00316 

— 

4 

Ethylene 
Carbon  bisulphide 

.02435 
.00429 

.02035 
.00396 

.01716 
.00367 

.01470 
.00342 

.OI28O 
.00319 

.OII24 

.OOS95 

•00733 

4 
4 

Carbon  dioxide  (liq.) 

.00099 

.00085 

.00071 

_ 

_ 

_ 

6. 

Chlorides  :  Propyl 

.00436 

.00390 

•00352 

.00319 

.00291 

- 

- 

- 

4 

Allyl 

.00402 

.00358 

.OO322 

.00292 

— 

— 

— 

— 

4 

.     Ethylene 

.01  1  28 

.00961 

•00833 

.00730 

.00646 

.00576 

.00470 

- 

4 

Chloroform 

.00700 

.00626 

.00564 

.00511 

.00466 

.00390 

— 

— 

4 

Ether 

— 

.0026 

.0023 

.0021 

— 

_ 

- 

i 

Ethylbenzole 

.00874 

•00758 

.00666 

.00592 

.00529 

•00477 

.00394 

.00330 

4 

Ethylsulphide 
Iodides:  Methyl 

.00559 
.00594 

.00496 
.00536 

.00444 
.00487 

.00401 
.00446 

.00363 
.00409 

.00331 

.00279 

.00237 
—  1 

4 

Ethyl 

.00719 

.00645 

•00583 

.00530 

.00484 

.00444 

.00378 

_ 

Propyl 
Allyl 

•00938 
.00930 

.00827 
.00819 

•00737 
.00726 

.00662 
.00652 

.00598 
.00588 

•00544 
•00534 

.00456 
.00448 

.00387 
.00381 

4 
4 

Metaxylol 

.00802 

.00698 

.OO6l5 

.00547 

.00491 

.00444 

.00369 

•00313 

4 

Nitrobenzene 

— 

— 

.0203 

.OI7O 

.0144 

.0124 

i 

Paraffines  :   Pentane 

.00283 

.00256 

.00232 

.00212 

- 

- 

- 

4 

Hexane 

.00396 

•00355 

.OO32O 

.OO29O 

.00264 

.00241 

.00221 

— 

4 

Heptane 

.00519 

.00460 

.OO4IO 

.00369 

.00334 

.00303 

.00253 

.OO2I4 

4 

Octane 

.00703 

.00612 

.00538 

.00478 

.00428 

.00386 

.00318 

.OO266 

4 

Isopentane 

.00273 

.00246 

.00223 

.00204 

— 

— 

— 

— 

4 

Isohexane 

.00371 

•00332 

.OO3OO 

.OO272 

.00247 

.00226 

- 

- 

4 

Isoheptane 

.00477 

.00423 

•00379 

.00342 

.00309 

.00282 

.00235 

.00200 

4 

Propyl  aldehyde 
Toluene 

.00768 

.0047 
.00668 

.0041 
.00586 

.0036 
.00520 

•°°33 
.00466 

.00420 

.00348 

.OO292 

i 

4 

i  Pribram-Handl,  Wien.  Ber.  78,  1878,  80,  1879,  84,                1897;    Proc.  Roy.  Soc.  55,  1894,  60,  1896;  Jour. 
x88i.                                                                                     Chem.  Soc.  71,  1897  ;  Chem.  News,  75,  1897. 

a  Gartenmeister,  Zeitschr.  Phys.  Chem.  6,  1890.               5  Wijkander,  Wied.  Beibl.  3,  1879. 
3  Rellstab,  Diss.  Bonn,  1868.                                              6  Warburg-Babo,  Wied.  Ann.  17,  1882. 

4  Thorpe-Roger,  Philos.  Trans.  185  A,  1894,  189  A, 

*  Calculated  from  the  specific  viscosities  given  in  Landolt  &  Bernstein's  Phys.  Chem.  Tab. 

For  inorganic  acids,  see  Solutions. 
SMITHSONIAN  TABLES. 


TABLE  1 1 3. 
VISCOSITY  OF  SOLUTIONS. 


129 


This  table  is  intended  to  show  the  effect  of  change  of  concentration  and  change  of  temperature  on  the  viscosity  of 
solutions  of  salts  in  water.  The  specific  viscosity  X  100  is  given  for  two  or  more  densities  and  for  several  tem- 
peratures in  the  case  of  each  solution,  /x.  stands  for  specific  viscosity,  and  t  for  temperature  Centigrade. 


Salt. 

Percentage 
by  weight 
of  salt  in 
solution. 

Density. 

- 

t 

J* 

' 

- 

t 

f- 

t 

Authority. 

BaCl2 

7.60 

_ 

77-9 

10 

44.0 

30 

35-2 

So 

_ 

_ 

Sprung. 

" 

15.40 

- 

86.4 

" 

56.0 

M 

39-6 

u 

- 

- 

" 

" 

24-34 

— 

100.7 

" 

66-2 

" 

47-7 

" 

— 

— 

" 

Ba(N03)2 

2.98 

1.027 

62.0 

15 

51.1 

25 

42-4 

35 

34-8 

45 

Wagner. 

5-24 

1.051 

68.1 

54-2 

" 

44.1 

II 

36-9 

CaCl2 

I5-I7 

- 

110.9 

IO 

7i-3 

30 

50-3 

So 

_ 

_ 

Sprang. 

" 

31.60 

— 

272.5 

M 

177.0 

124.0 

— 

— 

" 

" 

39-75 

- 

670.0 

• 

379-o 

" 

245-5 

u 

- 

- 

u 

M 

44.09 

- 

- 

- 

593-1 

*' 

363-2 

* 

— 

- 

" 

Ca(N03)2 

17-55 

I.I7I 

93-8 

15 

74-6 

25 

60.0 

35 

49-9 

45 

Wagner. 

« 

30.10 
40.13 

1.274 
1.386 

144.1 
242.6 

M 

112.7 
217.1 

« 

90.7 
156.5 

H 

75-i 
128.1 

- 

H 

CdCl2 

11.09 

I.IO9 

77-5 

15 

60.5 

25 

49.1 

35 

40.7 

45 

« 

- 

16.30 
24-79 

1.181 

1.320 

88.9 
104.0 

« 

III 

« 

47.2 
53-6 

« 

Cd(N03)2 

i7'8! 

1.074 

61.9 

15 

50.1 

25 

41.1 

35 

34-o 

45 

« 

" 

I-I59 

71.8 

« 

58.7 

48.8 

41-3 

11 

* 

22.36 

1.241 

85.1 

" 

69.0 

tt 

57-3 

" 

47-5 

" 

It 

CdSO4 

7.14 

i.  068 

78.9 

15 

61.8 

25 

49-9 

35 

41-3 

45 

tt 

" 

14.66 

1.159 

96.2 

« 

72-4 

58.1 

48.8 

tt 

" 

22.OI 

1.268 

120.8 

U 

91.8 

" 

73-5 

" 

60.  i 

" 

ft 

CoCl2 

7-97 

1.081 

83.0 

15 

65.1 

25 

53-6 

35 

44-9 

45 

ft 

" 

14.86 

1.161 

1  1  1.  6 

85.1 

73-7 

u 

58.8 

tt 

" 

22.27 

1.264 

161.6 

" 

126.6 

" 

101.6 

ft 

85.6 

H 

ft 

Co(N03)2 

8.28 

1.073 

74-7 

15 

§9 

25 

48.7 

35 

39-8 

45 

tt 

" 

15.96 

1.144 

87.0 

2 

|| 

55-4 

44-9 

tt 

M 

24-53 

1.229 

110.4 

" 

0 

" 

7i-5 

M 

59-  1 

" 

tf 

CoS04 

7-24 

1.086 

86.7 

15 

68.7 

25 

55-0 

35 

45-i 

45 

tt 

- 

14.16 
21.17 

I-I59 
1.240 

117.8 
193.6 

« 

95-5 
146.2 

« 

76.0 
113.0 

61.7 
89.9 

tf 
tt 

CuCl2 

I2.OI 

1.104 

87.2 

15 

67.8 

25 

SS-i 

35 

45-6 

45 

tt 

M 

2i-35 

1.215 

121.5 

95-8 

77-o 

M 

63-2 

tt 

U 

33-03 

178.4 

* 

137-2 

* 

107.6 

" 

87.1 

" 

tt 

Cu(N03)2 

18.99 

1.177 

97-3 

15 

76.0 

25 

61.5 

35 

5J-3 

45 

tt 

" 

26.68 

1.264 

126.2 

98.8 

" 

80.9 

" 

68.6 

" 

tf 

" 

46.71 

I-536 

382.9 

" 

283.8 

" 

215-3 

" 

172.2 

M 

ft 

CuS04 

6.79 

L055 

79-6 

15 

61.8 

25 

49-8 

35 

41.4 

45 

ft 

tt 

12.57 
17.49 

1.115 
1.163 

98.2 
124.5 

« 

74-o 
96.8 

U 

59-7 
75-9 

52.0 
61.8 

M 

tt 
tt 

HC1 

8.14 

16.12 

1-037 
1.084 

71.0 
80.0 

15 

£5 

2J 

48-3 
56-4 

35 

40.1 

48.1 

45 

H 

tt 
tt 

" 

23.04 

1.114 

91.8 

" 

79-9 

" 

65-9 

M 

564 

" 

tt 

HgCl2 

0.23 

1.023 

- 

- 

58-5 

20 

46.8 

3f 

38-3 

40 

tt 

" 

3-55 

'•033 

76.75 

10 

59-2 

46.6 

38-3 

ft 

SMITHSONIAN  TABLES. 


TABLE  1 1 3  (continued). 
VISCOSITY  OF   SOLUTIONS. 


Salt 

Percentage 
by  weight 
of  salt  in 
solution. 

Density. 

p 

/ 

V- 

t 

f* 

/ 

p 

/ 

Authority. 

HN08 

8-37 

1.067 

66.4 

IS 

54-8 

25 

45-4 

35 

37-6 

45 

Wagner. 

« 

M 

I2.2O 
28.31 

1.116 
1.178 

69.5 
80.3 

H 

« 

57-3 
65-5 

u 
« 

47-9 
54-9 

«« 

40.7 
46.2 

« 

u 
«( 

H2S04 

7.87 

1.065 

77-8 

is 

61.0 

25 

50.0 

35 

41.7 

45 

(( 

*s-s° 

1.130 

95-i 

(i 

75-o 

14 

60.5 

(i 

49-8 

u 

<« 

U 

2343 

i.  200 

122.7 

" 

95-5 

« 

77-5 

U 

64-3 

« 

(( 

KCl 

10.23 

- 

70.0 

10 

46.1 

30 

33-i 

50 

_ 

_ 

Sprung. 

« 

22.21 

— 

70.0 

« 

48.6 

36-4 

u 

— 

- 

44 

KBr 

I4.O2 

_ 

67.6 

10 

44.8 

3p 

32.1 

50 

_ 

_ 

(4 

« 

23.16 

— 

66.2 

« 

44-7 

33-2 

u 

— 

— 

tt 

« 

34-64 

- 

66.6 

« 

47.0 

tt 

35-7 

u 

- 

- 

ft 

KI 

8.42 

— 

69.5 

10 

44.0 

30 

3J-3 

50 

_ 

_ 

tt 

« 

17.01 

— 

65-3 

« 

42.9 

3i-4 

tt 

— 

— 

4t 

« 

33-°3 

— 

61.8 

« 

42.9 

« 

32-4 

«« 

— 

— 

tt 

« 
tt 

45-98 
54.00 

- 

63.0 
68.8 

It 

$5 

u 

u 

35-3 
37-6 

M 
«« 

- 

: 

tt 
tt 

KClOs 

3-51 

_ 

71.7 

10 

44-7 

30 

31-5 

5p 

_ 

_ 

It 

« 

5.69 

— 

— 

u 

45-o 

«( 

31-4 

— 

— 

tt 

KN08 

6.32 

- 

70.8 

10 

44-6 

30 

31.8 

Sf 

_ 

_ 

tt 

« 

12.19 

— 

68.7 

« 

44-8 

« 

32-3 

— 

— 

U 

« 

17.60 

- 

68.8 

« 

46.0 

u 

33-4 

f 

- 

- 

M 

K2SO4 

S-I7    , 

_ 

77-4 

IO 

48.6 

3p 

34-3 

Sf 

_ 

_ 

« 

u 

9-77 

— 

81.0 

u 

52-0 

36-9 

— 

— 

tt 

K2CrO4 

"•93 

_ 

75-8 

IO 

62.5 

3p 

41.0 

40 

_ 

_ 

ft 

« 

19.61 

_ 

85-3 

" 

68.7 

47-9 

M 

_ 

_ 

tt 

tt 

24.26 

1-233 

97-8 

« 

74-5 

«< 

54-5 

« 

- 

- 

Slotte. 

U 

32.78 

109.5 

H 

88.9 

44 

62.6 

(« 

- 

- 

Sprung. 

K2Cr207 

4.71 

1.032 

72.6 

10 

55-9 

20 

45-3 

30 

37-5 

40 

Slotte. 

H 

6.97 

1.049 

73-i 

It 

56-4 

u 

45-5 

«( 

37-7 

u 

tt 

LiCl 

7-76 

_ 

96.1 

10 

59-7 

3f 

41.2 

50 

_ 

_ 

Sprung. 

u 
« 

I3-9I 
26.93 

- 

121.3 
229.4 

« 
« 

75-9 
142.1 

ft 

52.6 
98.0 

« 
(« 

- 

- 

« 

Mg(N08)2 

18.62 

I.IO2 

99-8 

*5 

81.3 

25 

66.5 

35 

56.2 

45 

Wagner. 

«« 

34.19 

1.200 

213-3 

tt 

164.4 

« 

132.4 

p 

109.9 

H 

p 

M 

39-77 

1.430 

3!7-o 

u 

250.0 

« 

191.4 

« 

158.1 

If 

tt 

MgSO* 

4.98 

_ 

96.2 

IO  i 

59-o 

30 

40.9 

50 

_ 

_ 

Sprung. 

" 

9-5° 

— 

130.9 

tt 

77-7 

«< 

53-o 

u 

— 

— 

tt 

« 

19.32 

— 

302.2 

« 

166.4 

« 

1  06.0 

(( 

— 

— 

M 

MgCrO4 

12.31 

1.089 

111.3 

10 

84.8 

2O 

67.4 

30 

55-o 

40 

Slotte. 

H 

21.86 

1.164 

167.1 

It 

125-3 

« 

99.0 

a 

79-4 

« 

<< 

«( 

27.71 

I.2I7 

232.2 

tt 

172.6 

u 

T33-9 

u    , 

106.6 

«( 

tt 

MnCl2 

8.01 

1.096 

92.8 

15 

71.1 

25 

57-5 

35 

48.1 

45 

Wagner. 

tt 

15-65 

1.196 

130.9 

«< 

104.2 

" 

84.0 

68.7 

M 

<« 

3°-33 

1-337 

256-3 

it 

193.2 

" 

!55-o 

« 

123.7 

" 

M 

« 

40.13 

1-453 

537-3 

u 

393-4 

«( 

300.4 

tt 

246.5 

u 

ft 

SMITHSONIAN  TABLES. 


TABLE  113  (continued). 
VISCOSITY  OF  SOLUTIONS. 


Salt. 

Percentage 
by  weight 
of  salt  in 
solution. 

Density. 

> 

t 

" 

t 

- 

t 

- 

t 

Authority. 

Mn(NO3)2 

18.31 
29.60 

49-3  T 

I.I48 

1.323 
1.506 

96.0 

167-5 
396.8 

15 

76.4 

126.0 
301.1 

25 

64.5 

IO4.6 

22I.O 

35 

188^8 

45 

H 

Wagner. 
u 

MnS04 

ii-45 

I.I47 

129.4 

15 

98.6 

25 

78.3 

35 

63-4 

45 

(I 

" 

18.80 

1.251 

228.6 

172.2 

I37-I 

107.4 

H 

" 

22.08 

1.306 

661.8 

" 

474-3 

" 

347-9 

" 

266.8 

" 

U 

NaCl 

7-95 

- 

82.4 

10 

52.0 

30 

31-8 

5? 

- 

- 

Sprung. 

" 

I4-31 

— 

94-8 

" 

60.  i 

" 

36-9 

— 

— 

" 

" 

23.22 

— 

128.3 

" 

79-4 

" 

47-4 

f 

— 

— 

" 

NaBr 

9-77 

_ 

75-6 

10 

48.7 

3° 

34-4 

5° 

_ 

_ 

« 

" 

18.58 

- 

82.6 

" 

53-5 

" 

38.2 

" 

- 

- 

" 

" 

27.27 

- 

95-9 

" 

" 

43-8 

" 

- 

- 

" 

Nal 

8.83 

- 

73-i 

10 

46.0 

3° 

32-4 

So 

- 

- 

« 

" 

17-15 

— 

73.8 

" 

47-4 

" 

33-7 

" 

— 

— 

" 

H 

35-69 

- 

86.0 

" 

55-7 

" 

40.6 

" 

- 

- 

" 

" 

55-47 

- 

157-2 

" 

96.4 

" 

66.9 

" 

- 

- 

" 

NaClOs 

11.50 

_ 

78.7 

10 

50.0 

3° 

35-3 

5° 

_ 

_ 

« 

H 

20.59 

- 

88.9 

" 

56.8 

40.4 

- 

- 

" 

" 

33-54 

— 

I2I.O 

" 

75-7 

" 

53-o 

" 

— 

— 

" 

NaNOg 

7-25 

_ 

75-6 

IO 

47-9 

3° 

33-8 

5f 

_ 

_ 

« 

H 

I2-35  ' 

— 

81.2 

" 

51.0 

u 

36.1 

— 

— 

" 

K 

18.20 

- 

87.0 

121.  2 

« 

55-9 
76.2 

« 

39-3 
53-4 

I 

- 

: 

« 

Na2S04 

4.98 

- 

96.2 

10 

59-o 

3o 

40.9 

5° 

- 

- 

« 

" 

9-50 

— 

170.9 

" 

77-7 

M 

53-o 

u 

— 

— 

" 

" 

14.03 

— 

187.9 

u 

107.4 

" 

71.1 

* 

— 

— 

M 

" 

19.32 

- 

3O2.2 

" 

166.4 

" 

1  06.0 

" 

- 

- 

" 

Na2CrO4 

5-76 

1.058 

85.8 

10 

66.6 

20 

53-4 

1? 

43-8 

40 

Slotte. 

u 

10.62 

1.  112 

I03-3 

" 

79-3 

" 

63-5 

52-3 

" 

" 

" 

14.81 

1.164 

127-5 

" 

97.1 

" 

77-3 

" 

63.0 

" 

" 

NH4C1 

3-67 

_ 

7i-5 

10 

45-o 

30 

3i.9 

So 

- 

- 

Sprung. 

" 

8.67 

— 

69.1 

" 

45-3 

" 

32.6 

H 

— 

— 

" 

" 

15.68 

— 

67-3 

M 

46.2 

" 

34-o 

" 

— 

— 

" 

" 

23-37 

— 

67.4 

" 

47-7 

" 

36-1 

" 

— 

— 

" 

NH4Br 

15-97 

_ 

65.2 

IO 

43-2 

30 

31.5 

50 

- 

- 

M 

" 

25-33 

— 

62.6 

" 

43-3 

32-2 

— 

— 

" 

" 

36.88 

- 

62.4 

* 

44-6 

H 

34-3 

" 

- 

- 

M 

NH4NO3 

5-97 

_ 

69.6 

10 

44-3 

30 

31.6 

5° 

_ 

_ 

M 

" 

12.19 

— 

66.8 

" 

44-3 

3T-9 

" 

— 

— 

" 

" 

27.08 

- 

67.0 

* 

47-7 

H 

349 

« 

- 

- 

" 

* 

37-22 

— 

71.7 

" 

51.2 

" 

38.8 

" 

— 

— 

" 

* 

— 

81.1 

H 

63-3 

48.9 

" 

— 

— 

*' 

(NH4)2S04 

8.10 

- 

107.9 

10 

52-3 

3° 

37-o 

50 

- 

_ 

« 

" 

J5-94 

— 

1  20.  2 

" 

60.4 

" 

43-2 

" 

— 

— 

" 

25-5I 

~ 

I48.4 

M 

74-8 

54-i 

M 

SMITHSONIAN  TABLES. 


132 


TABLE  113  (continued). 
VISCOSITY   OF   SOLUTIONS, 


Salt 

Percentage 
by  weight 
of  salt  in 
solution. 

Density. 

M 

I 

* 

t 

I" 
M 

t 

M 

t 

Authority. 

(NH4)2Cr04 

10.52 

1.063 

79-3 

10 

62.4 

20 

_ 

_ 

424 

40 

Slotte. 

« 

19-75 
28.04 

1.  120 
I.I73 

00,2 
IOI.I 

« 

70.0 
80.7 

« 

57-8 
60.8 

3° 

48.4 
56-4 

- 

H 

(NH4)2Cr207 

6.85 
13.00 

1.039 

1.078 

72-5 

72.6 

10 

56.3 

57-2 

20 

45-8 
46.8 

3? 

38.0 

39-  1 

4p 

M 

M 

19-93 

I.I26 

77-6 

" 

58.8 

" 

48.7 

" 

40.9 

" 

*' 

1  NiCl2 

11.45 

I.I09 

90.4 

15 

70.0 

25 

57-5 

35 

48.2 

45 

Wagner. 

ftf 

22.69 

1.226 

140.2 

(4 

109.7 

U 

87.8 

(t 

72.7 

" 

" 

ff 

30.40 

1-337 

229.5 

n 

171.8 

" 

139.2 

« 

111.9 

" 

" 

Ni(N08)2 

16.49 

1.136 

90.7 

15 

70.1 

25 

57-4 

35 

48.9 

45 

« 

« 

3O.OI 
40.95 

1.278 
1.388 

135-6 

222.6 

« 

105.9 
169.7 

H 

128.2 

70.7 
152.4 

a 

« 

H 

NiSO4 

10.62 

1.092 

94.6 

I5 

73-5 

25 

60.  i 

35 

49-8 

45 

ft 

M 

18.19 

1.198 

154-9 

" 

119.9 

(i 

99-5 

75-7 

• 

" 

25-35 

1-3*4 

298.5 

" 

224.9 

* 

" 

152.4 

" 

u 

Pb(N08)2 

17-93 

1.179 

74.0 

15 

59-  T 

25 

48.5 

35 

40.3 

45 

« 

" 

32.22 

1.362 

91.8 

« 

72.5 

U 

59-6 

50.6 

" 

Sr(N08)2   1 

10.29 

i.  088 

69-3 

15 

56.0 

25 

45-9 

35 

39-  ! 

45 

« 

" 

21.19 

1.124 

87-3 

69.2 

57-8 

48.1 

M 

" 

" 

32.6l 

1.307 

II6.9 

" 

93-3 

" 

76.7 

" 

62.3 

U 

(i 

ZnCl2 

15-33 

1.146 

93-6 

15 

72.7 

25 

57-8 

35 

48.2 

45 

« 

" 

23-49 

1.229 

111.5 

« 

86.6 

69.8 

57-5 

" 

'* 

33-78 

J-343 

M 

117.9 

" 

90.0 

H 

72.6 

H 

M 

Zn(N08)2 

15-95 

1.115 

80.7 

15 

64-3 

25 

52.6 

35 

43-8 

45 

« 

" 

1.229 

104.7 

II 

85-7 

« 

69.5 

H 

57-7 

" 

" 

44-5° 

1-437 

167.9 

" 

130.6 

* 

105.4 

(i 

87.9 

" 

" 

ZnS04 

7.12 

1.106 

97.1 

15 

79-3 

25 

62.7 

35 

5T-5 

45 

« 

« 

16.64 
23.09 

1.281 

156.0 
232.8 

« 

u 

177-4 

a 

94-2 

M 

73-5 
108.1 

« 

SMITHSONIAN  TABLES. 


TABLE  114. 
SPECIFIC   VISCOSITY.* 


133 


Dissolved  salt. 

Normal  solution. 

J  normal. 

J  normal. 

£  normal. 

Authority. 

4 
1 

Specific 
viscosity. 

£, 

3 

P 

&£ 

11 
W5 

£ 

•a 

1 

Specific 
viscosity. 

>> 
"53 

y  ,»j» 

Acids:  C12O8     .    . 

1.0562 

.012 

1.0283 

1.003 

1.0143 

I.OOO 

1.0074 

0-999 

Reyher. 

HC1  .     .    . 

1.0177 

.067 

1.0092 

1.034 

1.0045 

I.OI7 

I.OO25 

1.009 

tt 

HC1O3   .     . 

1.0485 

.052 

1.0244 

1.025 

1.0126 

I.OI4 

1.0064 

1.006 

« 

HNO3    .     . 

1.0332 

.027 

1.0168 

I.OII 

1.0086 

I.OO5 

1.0044 

1.003 

« 

H2SO4    .     . 

1.0303 

.090 

1.0154 

1.043 

1.0074 

I.O22 

1-0035 

1.008 

Wagner. 

Aluminium  sulphate 

1-0^50 

.406 

1.0278 

1.178 

1.0138 

I.082 

1.0068 

1.038 

« 

Barium  chloride  .     . 

1.0884 

.123 

1.0441 

1-057 

1.0226 

1.026 

I.OII4 

1.013 

« 

"        nitrate     .     . 

_ 

1.0518 

1.044 

1.0259 

I.  O2  1 

I.OI30 

1.008 

M 

Calcium  chloride 

1.0446 

.i~56 

1.0218 

1.076 

1.0105 

1.036 

1.0050 

1.017 

« 

"        nitrate  .     . 

1.0596 

.117 

1.0300 

1.053 

1.0151 

I.  O2  2 

1.0076 

i.  008 

« 

Cadmium  chloride  . 

1.0779 

I-I34 

1.0394 

1.063 

1.0197 

I.03I 

1.0098 

i.  020 

« 

"          nitrate 

1.0954 

1.165 

1.0479 

1.074 

1.0249 

1.038 

I.OII9 

1.018 

M 

"         sulphate  . 

1-0973 

1.348 

1.0487 

1.157 

1.0244 

1.078 

I.OI20 

I-°33 

« 

Cobalt  chloride  .    . 

1.0571 

1.204 

1.0286 

1.097 

1.0144 

1.048 

1.0058 

1.023 

« 

"      nitrate      .    . 

1.0728 

1.166 

1.0369 

1-075 

1.0184 

1.032 

1.0094 

1.018 

« 

"      sulphate  .     . 

1.0750 

2-354 

1.0383 

1.160 

1.0193 

1.077 

I.OIIO 

1.040 

« 

Copper  chloride  .     . 
"        nitrate     .     . 

1.0624 
1>°75S 

1.205 
1.179 

1-0313 

1.0372 

1.098 
1.080 

1.0158 
1.0185 

1.047 
I.O4O 

1.0077 

1.0092 

1.027 
1.018 

« 

« 

"        sulphate 

1.0790 

I-358 

1.0402 

1.160 

1.0205 

1.  080 

1.0103 

1.038 

M 

Lead  nitrate    .     .     . 

1.1380 

I.IOI 

0.0699 

1.042 

I-°35I 

I.OI7 

1.0175 

1.007 

tt 

Lithium  chloride 

.0243 

1.142 

1.0129 

i.  066 

1.0062 

I.O3I 

1.0030 

I.OI2 

« 

"        sulphate     . 

•0453 

1.290 

1.0234 

I-I37 

1.0115 

1.065 

1.0057 

1.032 

« 

Magnesium  chloride 

•'375 

1.  201 

1.0188 

1.094 

1.0091 

1.044 

1.0043 

1.  02  1 

« 

"           nitrate  . 

.0512 

I.I7I 

1.0259 

1.082 

1.0130 

I.O4O 

1.0066 

I.O2O 

« 

"           sulphate 

.0584 

I  -367 

1.0297 

1.164 

1.0152 

1.078 

1.0076 

1.032 

« 

Manganese  chloride 

•0513 

I.2O9 

1.0259 

1.098 

1.0125 

1.048 

1.0063 

I.O23 

M 

"           nitrate  . 

.0690 

1.183 

1-0349 

1.087 

1.0174 

1.043 

1.0093 

1.023 

H 

"           sulphate 

.0728 

1.364 

1.0365 

1.169 

1.0179 

1.076 

1.0087 

1.037 

tt 

Nickel  chloride   .    . 

.0591 

I.2O5 

1.0308 

1.097 

1.0144 

1.044 

1.0067 

I.  O2  1 

« 

"      nitrate.    .    . 

•°755 

I.lSo 

1.0381 

1.084 

1.0192 

I.O42 

1.0096 

I.OI9 

« 

"       sulphate  .     . 
Potassium  chloride  . 

•0773 
.0466 

1.361 
0.987 

1.0391 
1.0235 

1.161 
0.987 

1.0198 
1.0117 

1-075 
0.990 

1.0017 

1.0059 

1.032 
0.993 

M 

« 

"          chromate 

•0935 

I.II3 

1-0475 

1-053 

1.0241 

I.O22 

I.OI2I 

1.  01  2 

II 

"          nitrate    . 
sulphate 

.0605 
1.0664 

0-975 
1.105 

1-0305 
1-0338 

0.982 
1.049 

1.0161 

1.0170 

0.987 
1.  02  1 

1.0075 
1.0084 

0.992 

1.008 

tt 

« 

Sodium  chloride  .     . 

1.0401 

1.097 

1.0208 

1.047 

1.0107 

I.O24 

1.0056 

1.013 

Reyher. 

"        bromide  .     . 

1.0786 

1.064 

1.0396 

1.030 

1.0190 

I.OI5 

I.OIOO 

1.008 

" 

"        chlorate      . 

1.0710 

1.090 

1.0359 

1.042 

1.0180 

I.O22 

1.0092 

I.OI2 

« 

"        nitrate    .     . 

1-0554 

1.065 

1.0281 

1.026 

1.0141 

I.OI2 

1.0071 

I.OO7 

* 

Silver  nitrate  .    ,    . 

1.1386 

1.058 

1.0692 

i.  020 

1.0348 

1.  006 

1.0173 

I.OOO 

Wagner. 

Strontium  chloride  . 

1.0676 

1.141 

1.0336 

1.067 

1.0171 

1.034 

1.0084 

I.OI4 

H 

"          nitrate    . 

1.0822 

1.115 

1.0419 

1.049 

1.0208 

1.024 

1.0104 

I.OII 

tt 

Zinc  chloride  .     .     . 

1.0590 

1.189 

1.0302 

1.096 

1.0152 

1-053 

1.0077 

1.024 

tt 

"     nitrate     .     .     . 

1.0758 

1.164 

1.0404 

1.086 

1.0191 

1.039 

1.0096 

I.OI9 

tt 

"    sulphate  .    .    . 

1.0792 

1-367 

1.0402 

i-i73 

1.0198 

1.082 

1.0094 

1.036 

« 

*  In  the  case  of  solutions  of  salts  it  has  been  found  (vide  Arrhennius,  Zeits.  fur  Phys.  Chem.  vol.  i,  p.  285)  that 
the  specific  viscosity  can,  in  many  cases,  be  nearly  expressed  by  the  equation  /A=/n1n,  where  p^  is  the  specific  viscosity 
for  a  normal  solution  referred  to  the  solvent  at  the  same  temperature,  and  n  the  number  of  gramme  molecules  in  the 
solution  under  consideration.  The  same  rule  may  of  course  be  applied  to  solutions  stated  in  percentages  instead  of 
gramme  molecules.  The  table  here  given  has  been  compiled  from  the  results  of  Reyher  (Zeits.  fiir  Phys.  Chem.  vol.  2, 
p.  749)  and  of  Wagner  (Zeits.  fur  Phys.  Chem.  vol.  5,  p.  31)  and  illustrates  this  rule.  The  numbers  are  all  for  25°  C 


SMITHSONIAN  TABLES. 


134  TABLE  11 5. 

VISCOSITY  OF  GASES  AND  VAPORS. 

The  values  of  /*  given  in  the  table  are  io6  times  the  coefficients  of  viscosity  in  C.  G.  S.  units. 


Substance. 

Temp. 

- 

Refer- 
ence. 

Substance. 

Temp. 

*. 

Refer- 
ence. 

Acetone 

18.0 

78. 

I 

Chloroform 

0.0 

95-9 

I 

Air 

-21.4 

163.9 

2 

" 

17.4 

102.9 

" 

.                 . 

o.o 

J73-3 

" 

"       . 

6l.2 

189.0 

3 

. 

15.0 

180.7 

M 

Ether 

0.0 

68.9 

.                 • 

99.1 

220.3 

" 

.        . 

16.1 

73-2 

" 

.                 . 

182.4 

255-9 

If 

it 

36.5 

79-3 

• 

Alcohol  :  Methyl 
Ethyl 

302.0 
66.8 
78.4 

299-3 
135- 
142. 

?, 

Ethyl  iodide      . 
Helium 

72-3 

0.0 

216.0 
189.1 
196.9 

3 

5 

Propyl,  norm. 

97-4 

142. 

" 

"          .        . 

66.6 

234.8 

«» 

Isopropyl 

82.8 

162. 

M 

«          t 

184.6 

269.9 

(4 

Butyl,  norm.    . 
Isobutyl  . 

116.9 

108.4 

143- 
144. 

M 

Hydrogen  . 

-20.6 

15.0 

81.9 
88.9 

2 

H 

Tert.  butyl      . 

82.9 

160. 

" 

M 

99-2 

105.9 

«» 

Ammonia 

0.0 

96. 

4 

" 

182.4 

121.5 

H 

"                      •        • 

20.0 

108. 

"              . 

302.0 

139.2 

« 

Argon    . 

O.O 

210.4 

5 

Mercury    . 

270.0 

489-* 

8 

u 

147 

220.8 

«                    i 

300.0 

532-* 

" 

u 

17.9 

99-7 

224.1 
273-3 

" 

; 

330-0 
360.0 

582* 
627* 

" 

M 

183-7 

322.1 

H 

. 

390.0 

671.* 

" 

Benzole  . 

19.0 

79- 

6 

Methane   . 

20.0 

1  20.  i 

4 

if 

Carbon  bisulphide 

IOO.O 

16.9 

118. 
92.4 

i 

Methyl  iodide   . 
"      chloride 

44-0 
I5.0 

232. 
105.2 

3 

2 

"       dioxide     . 

-20.7 

129.4 

2 

"           " 

3O2.O 

213.9 

" 

«                u 

15.0 

J45-7 

" 

Nitrogen  . 

-21.5 

156-3 

7 

. 

99.1 

1  86.  i 

" 

*'         .        . 

IO-9 

170.7 

" 

"              "             .          . 

182.4 

222.1 

« 

"         .        . 

53-5 

189.4 

w 

"           " 

302.0 

268.2 

" 

Oxygen     . 

15-4 

M 

"       monoxide 

0.0 

163.0 

4 

. 

53-5 

215.9 

H 

"              " 

20.0 

184.0 

" 

Water  vapor     . 

o.o 

90.4 

I 

Chlorine 

0.0 

128.7 

* 

«          <« 

16.7 

96.7 

* 

.        .        .        . 

2O.O 

147.0 

• 

IOO.O 

132.0 

9 

I  Puluj,  Wien.  Ber.  69,  (2),  1874.                        6  Schumann,  Wied.  Ann.  23,  1884. 

2  Breitenbach,  Ann.  Phys.  5,  1901.                      7  Obermayer,  Wien.  Ber.  71,  (2a),  1875. 
3  Steudel,  Wied.  Ann.  16,  1882.                         8  Koch,  Wied.  Ann.  14,  1881,  19,  1883. 

4  Graham,  Philos.  Trans.  Lond.  1846,  III.         9  Meyer-Schumann,  Wied.  Ann.  13,  1881. 

5  Schultze,  Ann.  Phys.  (4),  5,  6,  1901. 

*  The  values  here  given  were  calculated  from  Koch's  table  (Wied.  Ann.  vol.  19,  p.  869)  by  the  formula  JA  =  489  [i 
746(^-270)]. 

SMITHSONIAN  TABLES. 


TABLE  116.  135 

COEFFICIENT  OF  VISCOSITY  OF  GASES. 

Temperature  Coefficients. 

If  m=the  viscosity  at  f>  C.,  /io=the  vicosity  at  o°,  a=  the  coefficient  of  expansion,  |3, 7,  and 
=  coefficients  independent  of  t,  then 

(I)  fAt=fjLo(i-\-a/)n.    (Meyer,  Obermayer,  Puluj,  Breitenbach.) 

(II)      *=Ato(i+/8/).     (Meyer,  Obermayer.) 

(Ill)     =/io(i-fa/)*(i-r-7/)2.    (Schumann.) 


(IV)     =, 


J-.    (Sutherland.) 


Gas. 

Moio7. 

0, 

Constants. 

Range  °C. 

Refer- 
ence. 

Air 

_ 

0.003665 

«=o.77 

O-IOO 

I 

« 

I733-I 

.003665 

C=n9.4 

- 

2 

u 

u 

1811. 
2208. 

™* 

n=  0.7  544 

15.0-99.7 
99.7-182.9 

3 

u 

— 

— 

n  =0.7  54;  (7=111.3 

4 

Argon 

2208. 

_ 

72=0.815;  (7=150.2 
72=0.8227;  £'=169.9 

15-100 
14.7-99.7 

4 
3 

"              . 

2733. 

— 

72=0.8119 

99.7-183.7 

3 

Benzole 

698.4 

.004 

7=0.00185 

18.7-100 

5 

Carbon  dioxide 

1387.9 

(7=239.7 

_ 

8 

«           ti 

1497.2 

.003701 

7=0.000889 

I2.8-IOO 

5 

u              «« 

"       monoxide 
Ether  . 

1382.1 

IO2"5.2 
689. 

.OO37OI 
.003665 
.004158 

18=0.00348;  n=  0.941 
18=0.00269;  72=0.738 
72=0.94 

—21.5-53.5 
17.5-53-5 
0-36.5 

7 

8 

Ethylene 

961.3 

— 

6 

"        chloride 

922.2 
889.03 

.003665 
.OO39OO 

)8=  0.003150;  72=0.958 
18=0.00381  ;  72=0.9772 

—21.5-53-5 

1  5-6-i  57.3 

7 

Helium 

— 

— 

«=o.68i;  £=72.2 

0-15.0 

4 

M 

1969. 

— 

72=0.6852;  £"=80.3 

15.3-99.6 

3 

lt                     . 

2348. 

— 

n=  0.677  l 

99.6-184.6 

3 

Hydrogen    . 

8574 

.00366 

£"=71.7 

- 

2 

"            , 

— 

— 

7/=o.68i  ;  £"=72.2 

— 

4 

Mercury 

l62O. 

.003665 

72=1.6 

273-380 

10 

Nitrogen 

1658.6 

.003665 

18=0.00269;  77=0.738 

—21.5-53-5 

7 

Nitrous  oxide 

1353-3 

.003719 

18=0.00345;  72=0.929 

—  21.5-100.3 

M 

Oxygen 

— 

n  =0.782;  £"=128.2 

— 

4 

i  Holman,  Proc.  Amer.  Acad.  12,  1876;  21,          5  Schumann,  Wied.  Ann.  23,  1884. 

1885;  Philos.  Mag.  (5)  3,  1877;  21,  1886.           6  Breitenbach,  Ann.  Phys.  5,  1901. 
2  Breitenbach,  Wied.  Ann.  5,  1901.                         7  Obermayer,  Wien.  Ber.  73  (2A),  1876. 

3  Schultze,  Ann.  Phys.  (4)  5,  1901.                          8  Puluj,  Wien.  Ber.  78  (2),  1878. 

4  Rayleigh,  Proc.  Roy.  Soc.  62,  1897  ;  66,           9  Schultze,  Ann.  Phys.  (4)  6,  1901. 

1900;  67,  1900.                                                 10  Koch,  Wied.  Ann.  19,  1883. 

Compiled  from  Landolt-Bornstein-Meyerhoffer's  Physikalisch-chemische  Tabellen. 
SMITHSONIAN  TABLES. 


136  TABLE  11  7. 

DIFFUSION  OF  AN  AQUEOUS  SOLUTION  INTO  PURE  WATER. 

If  k  is  the  coefficient  of  diffusion,  dS  the  amount  of  the  substance  which  passes  in  the  time  dtt 
at  the  place  x,  through  q  sq.  cm.  of  a  diffusion  cylinder  under  the  influence  of  a  drop  of  concen- 
tration del dx^  then  . 

*.-**£* 

k  depends  on  the  temperature  and  the  concentration,  c  gives  the  gram-molecules  per  litre. 
The  unit  of  time  is  a  day. 


Substance. 

c 

t° 

k 

£8 

v  c 

(X  « 

Substance. 

<r 

t° 

k 

«8 

"w  q 

«  « 

Bromine  .        .        • 

O.I 

12. 

0.8 

I 

Calcium  chloride     . 

0.864 

8.5 

0.70 

4 

Chlorine  .        .        . 

•• 

12. 

1.22 

« 

K             «< 

1.22 

9- 

0.72 

Copper  sulphate 

" 

I?- 

o-39 

2 

«             «< 

0.060 

9- 

0.64 

M 

Glycerine 

a 

10.14 

°-357 

3 

«<             (i 

0.047 

9- 

0.68 

11 

Hydrochloric  acid   . 

« 

I9.2 

2.21 

2 

Copper  sulphate 

i-95 

17- 

0.23 

2 

Iodine 

<i 

12. 

(0.5) 

I 

u            <{ 

o-95 

17- 

0.26 

ii 

Nitric  acid 

H 

J9-5 

2.07 

2 

««            « 

0.30 

17- 

o-33 

ii 

Potassium  chloride  . 

" 

!7-5 

1.38 

2 

««            <« 

0.005 

17- 

0.47 

i« 

hydrate  . 

M 

'3-5 

1.72 

2 

Glycerine         •        . 

2/8 

10.14 

0-354 

3 

Silver  nitrate    .        . 

« 

12. 

0.985 

2 

"         .        •        • 

6/8 

10.14 

o.345 

Sodium  chloride 

" 

15.0 

0.94 

2 

ii 

10/8 

10.14 

0.329 

ii 

Urea 

U 

14.8 

0.97 

3 

<« 

14/8 

10.14 

0.300 

" 

Acetic  acid       .     (  . 
Barium  chloride 

O.2 
«< 

'i:5 

0.77 

0.66 

4 
4 

Hydrochloric  acid   . 

«             « 

4.52 
3.16 

»-S 

ii. 

2.93 
2.67 

4 

Glycerine          .     -  . 
Sodium  actetate 

« 

IO.I 
12. 

3-55 
0.67 

3 
5 

«<             K 

<i             <« 

0-945 
0.387 

ii. 
ii. 

2.12 

2.02 

«i 

"      chloride 

«« 

15.0 

0.94 

2 

«             t« 

0.2150 

ii. 

1.84 

« 

Urea 

ci 

14-8 

0.969 

3 

Magnesium  sulphate 

2.18 

5-5 

0.28 

4 

Acetic  acid 

1.0 

12. 

0.74 

6 

K               a 

0.541 

5-5 

0.32 

H 

Ammonia         . 

« 

lS-23 

!-54 

7 

««               «« 

3-23 

10. 

0.27 

" 

Formic  acid     . 

" 

12. 

0.97 

7 

U               U 

0.402 

IO. 

o-34 

It 

Glycerine 

M 

10.14 

0-339 

Potassium  hydrate  . 

0-75 

12. 

1.72 

6 

Hydrochloric  acid    . 

" 

12. 

2.09 

6 

«<               U 

0.49 

12. 

1.70 

" 

Magnesium  sulphate 
Potassium  bromide  . 

« 

7- 

10. 

0.30 
I-I3 

i 

«i               « 
"          nitrate    . 

0-375 
3-9 

12. 
I7.6 

1.70 
0.89 

it 

2 

"          hydrate  . 

II 

12. 

1.72 

6 

ii               it 

1.4 

I7.6 

I.IO 

ii 

Sodium  chloride 

« 

15.0 

0.94 

2 

U               <« 

o-3 

I7.6 

1.26 

<i 

«           « 

« 

M-3 

0.964 

3 

««                            K 

0.02 

I7.6 

1.28 

K 

"        hydrate      ! 
"        iodide 

(« 

12. 
10. 

i.  ii 

0.80 

2 

8 

"           sulphate 

o-95 
0.28 

19.6 
19.6 

0.79 
0.86 

K 

Sugar 
Sulphuric  acid 

<l 

12. 
12. 

0.254 

1.  12 

6 

6 

«<               «« 

K                              « 

0.05 

O.O2 

19.6 
19.6 

0.97 

I.OI 

II 

Zinc  sulphate  . 

M 

14.8 

0.236 

9 

Silver  nitrate    . 

3-9 

12. 

0-535 

" 

Acetic  acid 

2.0 

12. 

0.69 

6 

"           " 

0.9 

12. 

0.88 

(I 

Calcium  chloride     . 

« 

IO. 

0.68 

8 

II                       K 

0.02 

12. 

1.035 

(| 

Cadmium  sulphate  . 

M 

19.04 

0.246 

9 

Sodium  chloride 

2/8 

14-33 

1.013 

3 

Hydrochloric  acid    . 

« 

12. 

2.21 

6 

<«            ii 

4/8 

14-33 

0.996 

(i 

Sodium  iodide 

" 

IO. 

O.9O 

8 

<l                          K 

6/8 

14-33 

0.980 

2 

Sulphuric  acid 

K 

12. 

1.16 

6 

"                          "         . 

10/8 

14-33 

0.948 

* 

Zinc  acetate 

U 

18.05 

0.210 

9 

II                        « 

14/8 

'4-33 

0.917 

if 

«         <t 

(( 

O.O4 

O.I  2O 

9 

Sulphuric  acid 

9-85 

18. 

2.36 

2 

Acetic  acid 

3-° 

12. 

0.68 

(«                             K 

4.85 

18. 

1.90 

" 

Potassium  carbonate 

10. 

0.60 

8 

"                            " 

2.85 

1  8. 

i.  60 

«i 

"           hydrate  . 

« 

12. 

1.89 

6 

II                            «( 

0.85 

18. 

i-34 

(i 

Acetic  acid      . 

4.0 

12. 

0.66 

6 

««                            <« 

o-35 

18. 

1.32 

ii 

Potassium  chloride  . 

<i 

10. 

1.27 

8 

«                            (I 

0.005 

18. 

1.30 

(i 

i  Euler,  Wied.  Ann.  63,  1897.                                5  Kawalki,  Wied.  Ann.  52,  1894;  59,  1896.  . 

2  Thovert,  C.  R.  133,  1901  ;  134,  1902.                  6  Arrhenius,  Zeitschr.  Phys.  Chem.  10,  1892. 
3  Heimbrodt,  Diss.  Leipzig,  1903.                          7  Abegg,  Zeitschr.  Phys.  Chem.  n,  1893. 

4  Scheffer,  Chem.  Ber.  15,   1882;    16,   1883;      8  Schuhmeister,  Wien.  Ber.  79  (2),  1879. 

Zeitschr.  Phys.  Chem.  2,  1888.                         9  Seitz,  Wied.  Ann.  64,  1898. 

Compiled  from  Landolt-Bornstein-Meyerhoffer's  Physikalisch-chemische  Tabellen. 
SMITHSONIAN  TABLES. 


TABLE  118. 
DIFFUSION  OF  VAPORS. 


137 


Coefficients  of  diffusion  of  vapors  in  C.  G.  S.  units.    The  coefficients  are  for  the  temperatures  given  in  the  table  and 
a  pressure  of  76  centimetres  of  mercury.* 


Vapor. 

Temp.  C. 

0 

Jet  for  vapor 
diffusing  into 
hydrogen. 

Jet  for  vapor 
diffusing  into 
air. 

Jet  for  vapor 
diffusing  into 
carbon  dioxide. 

Acids  :  Formic         .... 

O.O 

0.5I3I 

0.1315 

0.0879 

"          '".«'• 

65.4 

0.7873 

0.2035 

0.1343 

"          '[  .',#     •    . 

84.9 

0.8830 

0.2244 

0.1519 

Acetic       !,,,:. 

O.O 

0.4040 

0.1061 

0.0713 

"           "  •     ;    . 

65.5 

O.62II 

0.1578 

0.1048 

"              «        • 

98.5 

0.7481 

0.1965 

0.1321 

Isovaleric    . 

0.0 

0.21  18 

0.0555 

0.0375 

.        •        •        »" 

98.0 

0.3934 

0.1031 

0.0696 

Alcohols:  Methyl    .... 

0.0 

0.5001 

0.1325 

0.0880 

«    ; 

25.6 

49.6 

0.6015 

0.6738 

0.1620 
0.1809 

0.1046 
0.1234 

Ethyl       '. 

O.O 

0.3806 

0.0994 

0.0693 

.... 

40.4 

0.5030 

0.1372 

0.0898 

"           .... 

66.9 

0.5430 

0.1475 

O.IO26 

Propyl     .... 

0.0 

0.3153 

0.0803 

0.0577 

. 

66.9 

0.4832 

0.1237 

0.0901 

"          .... 

83-5 

0.5434 

0.1379 

0.0976 

Butyl       .... 

0.0 

0.2716 

0.068  1 

0.0476 

u 

99.0 

0.5045 

0.1265 

0.0884 

Amyl       .... 

O.O 

0.2351 

0.0589 

0.0422 

"           .... 

99.1 

0.4362 

0.1094 

0.0784 

Hexyl      .... 

O.O 

0.1998 

0.0499 

0.0351 

. 

99.0 

0.3712 

0.0927 

0.0651 

O.O 

0.2940 

0.0751 

O.OC27 

o.  3400 

0.0877 

s 

0.0609 

u 

4CO 

w  J^.v^ 

0.3993 

O.IOII 

0.0715 

Carbon  disulphide    .... 

0.0 

*jsy*j 

0.3690 

0.0883 

0.0629 

"              "           .... 

19.9 

0.4255 

0.1015 

0.0726 

«             « 

32.8 

0.4626 

O.I  1  2O 

0.0789 

Esters  :  Methyl  acetate    . 
«            « 

0.0 

20.3 

0.3277 

0.3928 

0.1013 

0.0557 

0.0679 

Ethyl                   '.        '.        '. 

0.0 

0.2373 

0.0630 

0.04  co 

Ss-S 

"             "... 

46.1 

0.3729 

0.0970 

0.0666 

Methyl  butyrate  . 
Ethyl 

O.O 

92.1 

0.0 

96.5 

0.2422 

0.4308 
0.2238 
0.4112 

0.0640 

0.1139 
0.0573 

0.1064 

0.0438 
0.0809 
0.0406 
0.0756 

"     valerate     . 

0.0 

0.2050 

0.0505 

0.0366 

"          "           ... 

97.6 

0.3784 

0.0932 

0.0676 

O.O 

0.2960 

0.07  7  C 

O.OCC2 

19.9 

0.3410 

/  /  O 

0.0893 

J.J 
0.0636 

y  y 
O.O 

0.6870 

0.1980 

O.I3IO 

H 

4Q.C 

I.OOOO 

0.2827 

0.1811 

4 

tjrj 

92.4 

1.1794 

0-3451 

0.2384 

*  Taken  from  Winkelmann's  papers  (Wied.  Ann.  vols.  22,  23,  and  26).  The  coefficients  for  o°  were  calculated 
by  Winkelmann  on  the  assumption  that  the  rate  of  diffusion  is  proportional  to  the  absolute  temperature.  According 
to  the  investigations  of  Loschmidt  and  of  Obermeyer  the  coefficient  of  diffusion  of  a  gas,  or  vapor,  at  o°  C.  and  a 
pressure  of  76  centimetres  of  mercury  may  be  calculated  from  the  observed  coefficient  at  another  temperature  and 
pressure  by  the  formula  k0  =  &T(—Y^,  where  T  is  temperature  absolute  and  /  the  pressure  of  the  gas.  The 

exponent  n  is  found  to  be  about  1.75  for  the  permanent  gases  and  about  2  for  condensible  gases.    The  following 
are  examples:   Air  — CO2,   «=  1.968;   CO2— N2O,   «  =  2.o5;  CO2— H,  «=i.742;  CO  — O,  «==i.78s;  H  — O, 
«=  1.755;  O  —  N,  n-=.  1.792.     Winkelmann's  results,  as  given  in  the  above  table,  seem  to  give  about  2  for  vapors 
diffusing  into  air,  hydrogen  or  carbon  dioxide. 
SMITHSONIAN  TABLES. 


138  TABLES  1 19-11  QA. 

DIFFUSION   OF   GASES,  VAPORS,  AND   METALS. 

TABLE  119.  —  Coefficients  of  Diffusion  for  Various  Gases  and  Vapors.* 


Gas  or  Vapor  diffusing. 

Gas  or  Vapor  diffused  into. 

Temp. 
°C. 

Coefficient 
of  Diffusion. 

Authority. 

Air      

0 
0 
0 

o 

0 
0 
0 

o 

0 
0 
0 

o 

0 
0 
0 

o 
o 

0 
0 
0 

o 
o 

0 
0 

o 

0 
0 

o 

0 
0 

o 
8 
18 
18 

0.661 

0.1775 
0.1423 
0.1360 
0.1405 
0.1314 

0-5437 
0.1465 
0.0983 
0.1802 
0.0995 
0.1314 

O.IOI 

0.6422 

O.I  802 

0.1872 
0.0827 

0.3054 
0.6340 

0.5384 
0.6488 

0.4593 
0.4863 
0.6254 

0.5347 
0.6788 
0.1787 

0.1357 
0.7217 

0.1710 

0.4828 
0.2390 
0.2475 
0.8710 

Schulze. 
Obermayer. 

Lo  schmidt. 
Waitz. 
Loschmidt. 
Obermayer. 

tt 

Loschmidt. 

Stefan. 

Obermayer. 

« 

Loschmidt. 

Obermayer. 

Stefan. 
« 

Obermayer. 

• 

H 
« 
tt 
H 
« 

H 

Loschmidt. 
Obermayer. 
Loschmidt. 
Guglilemo. 
« 
« 

(< 

Carbon  dioxide             .    . 

U                         (4 
ft 
tt 

Carbon  disulphide        .    . 
Carbon  monoxide          .    . 

« 
Ether  .     ! 

Air      

u 

Carbon  monoxide      .    . 
«             « 

Hydrogen     .    .         .    . 

Nitrous  oxide   .... 
Oxygen 

Air  

Carbon  dioxide     .    .     . 

yj*  . 

Air  

tt 

Hydrogen        •    .         •    « 

Air  .              ..... 

H 

Carbon  dioxide      .     .    . 
"       monoxide      .    . 
Ethane     

Ethylene  

Nitrous  oxide   .... 
OxvEren 

Oxygen   . 

Carbon  dioxide     .    .     . 
Hydrogen          .... 

u 

Sulphur  dioxide    .... 
Water     

Air                     .... 

u 

H 

H 

Compiled  for  the  most  part  from  a  similar  table  in  Landolt  &  Bernstein's  Phys.  Chem.  Tab. 


TABLE  119 A. -Diffusion  of  Metals  Into  Metals. 

dv  ,</2z>     where  x  is  the  distance  in  direction  of  diffusion;  v,  the  degree  of  concentration  of 

dl  dx**    tfte  diffusing  metal;  /,  the  time;  k,  the  diffusion  constant  =  the  quantity  of  metal 

in  grammes  diffusing  through  a  sq.  cm.  in  a  day  when  unit  difference  of  concentra- 
tion (gr.  per  cu.  cm.)  is  maintained  between  two  sides  of  a  layer  one  cm.  thick. 


Diffusing  Metal. 

Dissolving 
Metal. 

Tempera- 
ture °  C. 

k. 

Diffusing  Metal. 

Dissolving 
Metal. 

Tempera- 
ture °  c. 

k. 

Gold     .     . 

Lead     . 

555 

3-T9 

Platinum  . 

Lead     . 

492 

1.69 

tt 

**        . 

492 

3.00 

Lead    .     . 

Tin  .    . 

555 

3.18 

tt 

u 

0.03 

Rhodium  . 

Lead     . 

55° 

3-04 

tt 

tt 

200 

0.008 

Tin       .     . 

Mercury 

1.22* 

tt 

u 

I65 

0.004 

Lead    .     . 

15 

1.0* 

tt 

tt 

100 

O.OOOO2 

Zinc     .     . 

15 

1.0* 

u 

Bismuth 

555 

4-52 

Sodium    . 

15 

0.45* 

tt 

Tin  .    . 

555 

4.65 

Potassium 

15 

0.40* 

Silver  .     . 

•     • 

555 

4.14 

Gold     .    . 

• 

15 

0.72* 

From  Roberts- Austen,  Philosophical  Transactions,  1896  A. 
*  These  values  are  from  Guthrie. 


SMITHSONIAN  TABLES. 


TABLE  120.  139 

SOLUBILITY  OF   INORGANIC   SALTS    IN   WATER;    VARIATION   WITH    THE 

TEMPERATURE. 

The  numbers  give  the  number  of  grammes  of  the  anhydrous  salt  soluble  in  1000  grammes  of 

water  at  the  given  temperatures. 


Salt. 

Temperature  Centigrade. 

0° 

10° 

20° 

30° 

40° 

5°° 

60° 

70° 

80° 

90° 

100° 

AgNO3  
A12(SO4)3    .... 
A12K2(S04)4    .     .     . 
A12(NH4)2(S04)4      . 
BoO<»  . 

1150 

3'3 
30 
26 
ii 
316 
50 
595 
405 
1614 

93 
1671 
818 
149 

744 
156 
43 
540 
1050 
285 

sli 

5° 
225 
1279 

133 

970 

7 
74 
127 

5f 
260 
408 

297 
119 
1183 
706 
795 

7i 
204 

356 
820 

317 
1630 
69 

25 
1590 
73° 

1600 
335 

45 
15 
333 
70 
650 
450 
1747 
149 

I731 

819 

208 
66 

312 

*S° 
609 

85 
277 
1361 
209 
1030 
9 
92 
127 

535 
3°9 
422 

333 
159 

730 

^ 

126 
263 

357 
§90 
502 
1700 
82 

J39 

1690 
805 

2I5O 
362 

66 

22 

357 
92 

745 
500 
1865 

23,° 
1787 

1250 

685 
918 
264 

74 
650 

343 
7i 
629 

131 

332 
1442 
3i6 

1120 
II 
III 
128 

545 
356 
439 
372 

2IO 

754 
903 

214 
335 
358 
990 
900 
1800 
96 

93 

1790 
880 

2700 
404 
84 
9i 

3*82 
116 

IOIO 

565 
1973 
339 
1841 

255 

330 
84 

1140 
373 

101 

650 

390 
1523 
45« 
1260 
14 
130 
129 

409 

453 
414 
270 
2418 
780 

39 
409 

435 
360 

1970 
in 
241 
1900 
962 

3350 

457 

124 
40 
408 
142 

"53 

650 
2080 
472 

295 

402 

96 
760 
1170 
401 

H5 
670 
292 

453 
1600 

639 
1360 
18 
148 
130 
575 
456 

458 

2970 
810 

1058 

(iaq) 
363 
1235 
960 

2200 
127 

639 
2050 
1049 

4000 
521 

159 

4~36 
171 

935 
2185 
644 
1949 

3~36 
820 

3$ 

"3 

I2IO 
429 
197 
690 

522 

T855 
1400 

22 
I65 
133 

504 

504 

3540? 
844 

1160 
105 

475 
367 

1050 
2480 
145 

2280 
1140 

4700 

59i 
248 

211 
62 

464 

1368 
940 
2290 
838 
1999 
1791 
390 

550 
139 

1270 

455 
260 
710 

|°5 
600 
1760 
1099 
1460 
26 
182 
p8 
610 

550 

552 

TO? 

1170 

200 

464 

371 
1470 
1150 
2830 
164 

2570 
1246 

270 
1417 

95° 
2395 
1070 
2050 

457 

560 
173 

1330 
483 
325 
730 

1840 
1380 
1510 

,| 

144 

596 

002 

5130? 
916 

244 

4~S8 
375 

3230 
949 

1360 

I 

6500 
73i 

352 
95 

524 
270 
1470 
960 
2500 
1340 
2103 
2078 

535 
1040 
5258 
506 
243 
955 
1400 

5I? 
396 

751 
73° 

1920 
1690 
1590 
38 
214 

& 

64* 
656 

5800 

953 
1185 

3M 

380 

1750 
1240 
3860 

2930 
1480 

7600 
808 

556 
306 

1527 

2601 
1630 
2149 

6*27 
1050 

43° 
37i 

1470 
538 
475 
771 

2OIO 
2040 
I680 

J 

689 
713 

7400 
992 

408 
452 

1610 

9100 

891 

1540 

T57 
588 
342 

1590 
1030 
2705 
1970 
2203 

j& 

5357 

540 
1050 
1560 
566 
560 
791 
1  020 

2090 
2460 
1780 

52 
241 

175 
730 

7~38 
773 

8710 

I033 
1205 

523 

452 
39i 
2040 
1260 
4330 

988 
3020 
I7S5, 

BaCl2           .... 

Ba(N03)2    .... 
CaCl2 

CoCl2      
CsCl  

CsNOg    
CsaSO4  . 

Cu(N03)2    .... 
CuSO4    

FeCl2  

Fe2Cl6     

FeSO4     

HsClo 

KBr    

KoCOi 

KC1    

KC1O3    

K2CrO4  
K2Cr2O7      .... 
KHCOs  
KI      

KNO3     

KOH      .              .     . 

K2PtCl6  

KoSCXi    , 

LiOH      

MgCl2     

MgS04    .     .       (7aq) 
.     .       (6aq) 
NH4C1    
NH4HCO3.     .    .    . 
NH4NO3     .... 
(NH4)2S04.     .     .     . 
NaBr                     .    . 

Na2B4O7      .... 
Na2CO3  .     .     (roaq) 
"        •     •      (7aq) 
NaCl            .     .     . 

NaC103  .     . 
Na2Cr04     . 
Na2Cr2O7    . 
NaHCO3     . 
Na2HPO4    . 
Nal 

NaNO3  

Compiled  from  Landolt-Bornstein-Meyerhoffer's  Physikaiisch-chemische  Tabellen. 

SMITHSONIAN  TABLES. 


140  TABLES  120  &***"«$ -i  22. 

SOLUBILITY  OF  SALTS  AND  GASES  IN  WATER. 

TABLE  120 (continued).  —  Solubility  of  Inorganic  Salts  In  Water;  Variation  with  the  Temperature. 

The  numbers  give  the  number  of  grammes  of  the  anhydrous  salt  soluble  in  1000  grammes  of 

water  at  the  given  temperatures. 


Salt. 

Temperature  Centigrade. 

0° 

10° 

20° 

30° 

40° 

50° 

60° 

70° 

80° 

Q0° 

100° 

NaOH      

420 

32 

141 

50 
I96 

S^S 

272 

3^ 

770 

'95 
364 
442 

395 
7 

2 

39 
27 
442 
948 

5*5 
39 

90 

305 

OIO 

600 

6 

444 
844 
330 
426 
483 

549 

10 

2 
62 

37 

1090 
62 
287 
194 

447 
700 
640 

8 

523 
911 

533 
482 

539 

10 

708 
14 

~£ 

49 

1190 

99 
400 

425 

12 

607 
976 
813 

535 
600 

12 
876 
2O 

4 

1290 
135 

495 
[482 

1026 
720 

694 

1035 
1167 

585 
667 

H 
9i3 
30 
40 
6 
209 
76 

2069 
700 

145° 
174 

468 

1697 
760 
502 
20 

787 
1093 

1556 
63I 

744 

926 
51 

2I 

304 
92 

7~68 

1740 

220 

455 
2067 
810 
548 
24 
880 
"55 

2000 
674 

831 
21 
940 

16 

10 

462 
109 
104 

255 

445 

594 
28 

977 
1214 
2510 

7H 
896 

956 
ii 

435 

127 

72 

8~9o 

3130 
300 

437 
2488 

632 

33 
1076 
1272 
3090 
75° 
924 
3° 
972 

16 

IIIO 

146 
69 

860 

429 
2542 

688 

1174 
i33i 
3750 
787 
962 

34 
990 

20 
2000 

I65 

58 

920 

330 
427 
2660 

7~76 
48 
1270 

1389 
5420 
818 
1019 
40 
ion 

4140 
47 

7~85 

Na^iPaOy  

Na2SO3    

Na2S04    .     .     (loaq) 
.     .      (7aq) 
Na2S2O3  

NiCJ2  

NiSO4               .    .     . 

PbBr2  

Pb(N03)2     .... 
RbCl   

RbNO3    

RboSOd   . 

SrCl2  

SnI2     

Sr(N03)2      .... 
Th(S04)2      .     .(Qaq) 

TICi'  .  .  :  :(4.aq). 

T1NO8     

T12SO4     

Yb2(S04)3    .... 
Zn(NO,)«     .... 
ZnSO4      

TABLE  121. -Solubility  of  a  Few  Organic  Salts  In  Water;  Variation  with  the  Temperature. 


Salt. 

0° 

10° 

20° 

30° 

40° 

50° 

60° 

70° 

80° 

90° 

100° 

H2(C02)2      .... 

36 

53 

102 

'59 

228 

321 

44^ 

63=; 

Q?8 

1  200 

_ 

H2(CH2.CO2)2      .    . 

28 

45 

69 

106 

162 

244 

35° 

511 

708 

- 

1209 

Tartaric  acid     .     .     . 

1150 

1260 

1390 

1560 

1760 

1950 

2180 

2440 

2730 

3070 

3430 

Racemic    "       ... 

92 

140 

206 

291 

433 

59  S 

783 

999 

1250 

!53o 

1850 

K(HC02)     .... 

2900 

335° 

3810 

455° 

575° 

7900 

KH(C4H404)   .     .     . 

3 

4 

6 

9 

13 

18 

24 

32 

45 

57 

69 

TABLE  122.— Solubility  of  Gases  in  Water;  Variation  with  the  Temperature. 

The  table  gives  the  weight  in  grammes  of  the  gas  which  will  be  absorbed  in  1000  grammes  of 
water  when  the  partial  pressure  of  the  gas  plus  the  vapor  pressure  of  the  liquid  at  the  given 
temperature  equals  760  mm. 


Gas. 

0° 

10° 

20° 

30° 

40° 

50° 

60° 

70° 

80° 

02 

.0705 

•0551 

•0443 

.0368 

.0311 

.0263 

.0221 

.0181 

•oi35 

H2 

N2 

.00192 

.0293 

.00174 

.0230 

,OOI6O 
.0189 

.00147 
.Ol6l 

.00138 
.0139 

.00129 

.0121 

.00118 
.0105 

.00102 
.0089 

.00079 
.0069 

Br2 

431- 

248. 

148. 

94. 

62. 

40. 

28. 

1  8. 

ii. 

C12 

9-97 

7-29 

5-72 

4-59 

3-93 

3-30 

2-79 

2.23 

C02 

3-35 

2.32 

1.26 

0.97 

0.76 

0.58 

— 

— 

H2S 

7.10 

5-3° 

3.98 

— 

— 

— 

— 

— 

— 

NH3 

689. 

535- 

422. 

- 

- 

- 

- 

- 

S02 

228. 

162. 

"3- 

78. 

54- 

~ 

Compiled  from  Landolt-Bornstein-Meyerhoffer's  Physikalisch-chemische  Tabellen. 
SMITHSONIAN  TABLES. 


TABLE  123. 
ABSORPTION  OF  CASES  BY  LIQUIDS.* 


141 


ABSORPTION  COEFFICIENTS,  a*,  FOR  GASES  IN  WATER. 

Temperature 

Centigrade. 

t 

Carbon 
dioxide. 
C02 

Carbon 
monoxide. 
CO 

Hydrogen. 
H 

Nitrogen. 

Nitric 
oxide. 
NO 

Nitrous 
oxide. 
N2O 

Oxygen. 

O 

1.797 

0-0354 

O.O2IIO 

0.02399 

0.0738 

1.048 

0.04925 

5 

1.430 

•03!5 

.02022 

.02134 

.0646 

0.8778 

•04335 

10 

1.185 

.0282 

.01944 

.01918 

.0571 

0.7377 

.03852 

iS 

1.002 

.0254 

.01875 

.01742 

•0515 

0.6294 

•03456 

20 

O.QOI 

.0232 

.01809 

.01599 

.0471 

0-5443 

•03137 

25 

0.772 

.0214 

.01745 

.01481 

.0432 

.02874 

3° 

.0200 

.01690 

.01370 

.0400 

— 

.02646 

40 

0.506 

.0177 

.01644 

.01195 

•°35  I 

- 

.02316 

5° 

.Ol6l 

.01608 

.01074 

•°3  *  5 

_. 

.02080 

100 

0.244 

.0141 

.OI6OO 

.01011 

.0263 

•• 

.01690 

Temperature 
Centigrade. 

t 

Air. 

Ammonia. 
NH3 

Chlorine. 
Cl 

Ethylene. 
C2H4 

Methane. 
CH4 

Hydrogen 
sulphide. 
H,S 

Sulphur 
dioxide. 
S02 

O 

0.02471 

II74.6 

3-036 

0.2563 

0.05473 

4-371 

79-79 

5 

10 

.02179 
•01953 

840.2 

2.8o8 
2.58S 

•2153 
•1837 

.04889 
.04367 

3.965 

6748 
56.65 

15 

•01795 

736.0 

2.388 

.1615 

.03903 

3-233 

47.28 

20 

.01704 

683.1 

2.156 

.1488 

.03499 

2.905 

39-37 

25 

610.8 

1.950 

.02542 

2.604 

32.79 

ABSORPTION  COEFFICIENTS,  at,  FOR  GASES  IN  ALCOHOL,  C,H5OH. 

Centigrade. 
t 

Carbon 
dioxide. 
C03 

Ethylene.  Methane.   Hydrogen. 
C2H4          CH4              H 

Nitrogen. 

Nitric 
oxide. 
NO 

Nitrous 
oxide. 
N20 

Hydrogen    Sulphur 
sulphide,     dioxide. 
H,S            S02 

0 

4.329 

3-595       0.5226       0.0692 

0.1263 

0.3161 

4.190 

17.89        328.6 

S 

3.891 

3.323         .5086         .0685 

.1241 

.2998 

3-838 

14.78        251.7 

IO 

3-5r4 

3.086       .4953        '°679 

.1228 

.2861 

3-525 

11.99      I9°-3 

15 

3-T99 

2.882         .4828         .0673 

.1214 

.2748 

3-215 

9-54       144-5 

20 

2.946 

2.713         .4710         .0667 

.1204 

.2659 

3-°  *  5 

7.41      114.5 

25 

2.756 

2.578         .4598          .0662 

.1196 

.2595 

2.819 

5.62       99.8 

*  This  table  contains  the  volumes  of  different  gases,  supposed  measured  at  o°  C.  and  76  centimetres'  pressure,  which 
unit  volume  of  the  liquid  named  will  absorb  at  atmospheric  pressure  and  the  temperature  stated  in  the  first  column. 
The  numbers  tabulated  are  commonly  called  the  absorption  coefficients  for  the  gases  in  water,  or  in  alcohol,  at  the 
temperature  /  and  under  one  atmosphere  of  pressure.  The  table  has  been  compiled  from  data  published  by  Bohr  & 
Bock,  Bunsen,  Carius,  Dittmar,  Hamberg,  Henrick,  Pagliano  &  Emo,  Raoult,  Schbnfeld,  Setschenow,  and  Winkler. 
The  numbers  are  in  many  cases  averages  from  several  of  these  authorities. 

NOTE. —The  effect  of  increase  of  pressure  is  generally  to  increase  the  absorption  coefficient.  The  following  is 
approximately  the  magnitude  of  the  effect  iti  the  case  of  ammonia  in  alcohol  at  a  temperature  of  23°  C. : 

f  P   =  45  cms.        50  cms.        55  cms.        60  cms.        65  cms. 

1 033  =  69  74  79  84  88 

According  to  Setschenow  the  effect  of  varying  the  pressure  from  45  to  85  centimetres  in  the  case  of  carbonic  acid  in 
water  is  very  small. 
SMITHSONIAN  TABLES. 


142 


TABLES  1 24-1 26. 
CAPILLARITY. -SURFACE   TENSION  OF  LIQUIDS.* 
TABLE  124.  -Water  and  Alcohol  in  Contact  with  Air. 


TABLE  126.  — Solutions  of  Salts  in 
Water,  t 


Surface  tension 
in   dynes   per 
centimetre. 

Surface  tension 
in   dynes  per 
centimetre. 

Surface 
tension 
in  dynes 

Salt  in 
solution. 

Density. 

Temp. 
C.° 

Tension 
in  dynes 
per  cm. 

Temp. 

Vx. 

Temp. 
C. 

Temp. 

timetre. 

Water. 

Ethyl 
alcohol. 

Water. 

Ethyl 
alcohol. 

Water. 

BaCl2 
CaCl2 

1.2820 
1.0497 

15-16 
15-16 

8l.8 

77-5 

0° 

5 

IO 

75-6 

74-9 
74-2 

23-5 
23.I 
22.6 

40° 

45 
5° 

70.0 

20.0 

*9-5 
I9.I 

80° 
85 

9° 

64-3 
63.6 
62.9 

« 

HC1 

« 

I-3511 

1-2773 
1.1190 
1.0887 

I9 
19 
20 

20 

95.0 

90.2 

73-6 

74-5 

15 

20 

$ 

22.2 
21-7 

13 

67.8 
6y.I 

18.6 
18.2 

95 

ICO 

62.2 
61.5 

KC1 

1.0242 
1.1699 

2O 
15-16 

IU 

25 
30 

35 

72.1 
71.4 
70.7 

21.3 
20.8 
20.4 

65 

70 

75 

66.4 
65.7 
65.0 

17.8 
17.3 

16.9 

: 

« 
MgCl2 

i.  ion 
1.0463 
1-2338 

15-16 
15-16 
15-16 

80.  i 
78.2 
90.1 

M 

1.1694 

15-16 

i  ^—  1  6 

85.2 
•780 

NaCl 

1.1932 

20 

85.8 

1.1074 

20 

80.5 

« 

1.0360 

2O 

77.6 

NH4C1 

1.0758 

16 

84-3 

TABLE  125.  -Miscellaneous  Liquids  in  Contact  with  Air. 

« 
SrCl2 

1-0535 
1.0281 

T     "JT  I  A 

16 
16 
j  c  1  6 

81.7 
78.8 
8c  6 

Liquid. 

Authority. 

« 

I.I2O4 

15-16 

05.0 
79-4 

Temp. 
C° 

tension 
in  dynes 

« 
K2C03 

1.0567 

I-3575 

15-16 
15-16 

77-8 
90.9 

per  cen- 

" 

1.1576 

15-16 

oi  .0 

« 

TVT_   r<(-) 

i  .0400 

15-16 

77.5 

1.1329 

14  15 

79-3 

Aceton    .... 
Acetic  acid  .     .     . 
Amyl  alcohol  .     . 

1  6.8 
17.0 
15.0 

23-3 
30.2 
24.8 

Ramsay-Shields. 
Average  of  various. 

it 

KNO3 

1.0605 
1.0283 
1.1263 

14-15 
14-15 
14 

77-8 
77-2 
78.9 

Benzene  .... 

IC.O 

28.8 

« 

1.0466 

14 

77-6 

Butyric  acid     .     . 

15.0 

28.7 

M 

NaN08 

1.3022 

12 

83-5 

Carbon  disulphide 
Chloroform      .     . 
Ether  

20.  o 

20.0 

20  o 

30-5 
28.3 
184 

Quincke. 

Average  of  various. 
u 

CuSO4 
« 

1.1311 

I-I775 
1.0276 

12 
15-16 
15-16 

80.0 
78.6 
77.0 

Glycerine    .     .     . 

17.0 

1.0.4 
63.14 

Hall. 

H2SO4 

1.8278 

15 

63.0? 

Hexane  .... 

0.0 

21.2 

Schiff. 

1-4453 

15 

79-7 

«< 

68.0 

14.2 

« 

1.2636 

15 

79-7 

Mercury  .... 
Methyl  alcohol     . 
Olive  oil  .     .     .     . 

1  8.0 
15.0 

20.0 

520.0 
24.7 
34.7 

Average  of  various. 
« 
« 

K2SO4 
« 

MgS04 

1.0744 
1.0360 
1.2744 

15-16 
15-16 
15-16 

78.0 

774 
83.2 

Petroleum  .     .    . 
Propyl  alcohol 

2O.O 

s-8 

25-9 
25-9 

Magie. 
Schiff. 

u 

Mn2SO4 

i.  0680 
1.1119 

15-16 
I5-l6 

77-8 
79.1 

« 

« 

97.1 

T8.0 

M 

'* 

1.0329 

15-16 

77-3 

Toluol     .... 

15.0 

29.1 

M 

ZnSO4 

1.3981 

I5-l6 

83-3 

« 

109.8 

18.9 

« 

M 

1.2830 

15-16 

80.7 

Turpentine  .    .     . 

21.0 

28.5 

Average  of  various. 

« 

1.1039 

15-16 

77-8 

*  This  determination  of  the  capillary  constants  of  liquids  has  been  the  subject  of  many  careful  experiments,  but  the 
results  of  the  different  experimenters,  and  even  of  the  same  observer  when  the  method  of  measurement  is  changed, 
do  not  agree  well  together.  The  values  here  quoted  can  only  be  taken  as  approximations  to  the  actual  values  for  the 
liquids  in  a  state  of  purity  in  contact  with  pure  air.  In  the  case  of  water  the  values  given  by  Lord  Rayleigh  from  the 
wave  length  of  ripples  (Phil.  Mag.  1890)  and  by  Hall  from  direct  measurement  of  the  tension  of  a  flat  film  (Phil.  Mag. 
1893)  have  been  preferred,  and  the  temperature  correction  has  been  taken  as  0.141  dyne  per  degree  centigrade.  The 
values  for  alcohol  were  derived  from  the  experiments  of  Hall  above  referred  to  and  the  experiments  on  the  effect  of 
temperature  made  by  Timberg  (Wied.  Ann.  vol.  30). 

The  authority  for  a  few  of  the  other  values  given  is  quoted,  but  they  are  for  the  most  part  average  values  derived 
from  a  large  number  of  results  published  by  different  experimenters. 

t  From  Volkmann  (Wied.  Ann.  vol.  17,  p.  353). 

SMITHSONIAN  TABLES. 


TABLES  1 27-1 29. 

TENSION   OF   LIQUIDS. 

TABLE  127. —Surface  Tension  of  Liquids.* 


143 


..!••!                                                 -'                                                            "                                                                                                                 '       '                                                      "  

Liquid. 

Specific 
gravity. 

Surface  tension  in  dynes  per  cen- 
timetre of  liquid  in  contact  with  — 

Air. 

Water. 

Mercury. 

Water    

I.O 

13-543 
1.2687 
14878 
0.7906 
0.9136 
0.8867 
9.7977 
1.  10 

1.1248 

75-o 
S'S-o 
3°-5 
01.8) 
(24.1) 
34-6 
28.8 
29.7 

(72.9) 
69.9 

O.O 
392.0 
41.7 
26.8 

18.6 

"•5 
(28.9) 

(392) 

(387) 
(415) 
364 

3'7 
241 

271 

(392) 
429 

Hyposulphite  of  soda  solution      .... 

TABLE  128.  — Surface  Tension  of  Liquids  at  Solidifying  Point.  1 


Substance. 

Tempera- 
ture of 
solidifi- 
cation. 
Cent.0 

Surface 
tension  in 
dynes  per 
centimetre. 

Substance. 

Tempera- 
ture of 
solidifi- 
cation. 
Cent.0 

Surface 
tension  in 
dynes  per 
centimetre. 

Platinum 

2000 

I69I 

Antimony 

432 

249 

Gold      . 

I2OO 

1003 

Borax    . 

IOOO 

216 

Zinc 

360 

877 

Carbonate  of  soda 

IOOO 

210 

Tin 

230 

599 

Chloride  of  sodium 

— 

116 

Mercury 

—40 

588 

Water   . 

o 

87.9* 

Lead     . 

330 

457 

Selenium 

217 

71.8 

Silver    . 

IOOO 

427 

Sulphur 

III 

42.1 

Bismuth 

265 

1390 

Phosphorus  . 

43 

42.0 

Potassium 

58 

Wax      . 

68 

34-i 

Sodium 

90 

258 

TABLE  129.  — Tension  of  Soap  Films. 


Elaborate  measurements  of  the  thickness  of  soap  films  have  been  made  by  Reinold  and 
Rucker.H  They  find  that  a  film  of  oleate  of  soda  solution  containing  i  of  soap  to  70  of 
water,  and  having  3  per  cent  of  KNOs  added  to  increase  electrical  conductivity,  breaks  at 
a  thickness  varying  between  7.2  and  14.5  micro-millimetres,  the  average  being  12.1  micro- 
millimetres.  The  film  becomes  black  and  apparently  of  nearly  uniform  thickness  round 
the  point  where  fracture  begins.  Outside  the  black  patch  there  is  the  usual  display  of 
colors,  and  the  thickness  at  these  parts  may  be  estimated  from  the  colors  of  thin  plates 
and  the  refractive  index  of  the  solution  (vide  Newton's  rings,  Table  146). 

When  the  percentage  of  KNO3  is  diminished,  the  thickness  of  the  black  patch  increases. 
For  example,  KNO3  =3  I  0.5  o.o 

Thickness  =  12.4  13.5  14.5  22.1  micro-mm. 

A  similar  variation  was  found  in  the  other  soaps. 

It  was  also  found  that  diminishing  the  proportion  of  soap  in  the  solution,  there  being 
no  KNO3  dissolved,  increased  the  thickness  of  the  film. 

I  part  soap  to  30  of  water  gave  thickness  21.6  micro-mm. 

I  part  soap  to  40  of  water  gave  thickness  22.1  micro-mm. 

I  part  soap  to  60  of  water  gave  thickness  27.7  micro-mm. 

I  part  soap  to  80  of  water  gave  thickness  29.3  micro-mm. 


*  This  table  of  tensions  at  the  surface  separating  the  liquid  named  in  the  first  column  and  air,  water  or  mercury 
as  stated  at  the  head  of  the  last  three  columns,  is  from  Quincke's  experiments  (Pogg.  Ann.  vol.  139,  and  Phil.  Mag. 
1871).  The  numbers  given  are  the  equivalent  in  dynes  per  centimetre  of  those  obtained  by  Worthington  from 
Quincke's  results  (Phil.  Mag.  vol.  20,  1885)  with  the  exception  of  those  in  brackets,  which  were  not  corrected  by 
Worthington ;  they  are  probably  somewhat  too  high,  for  the  reason  stated  by  Worthington.  The  temperature  was 
about  20°  C. 

t  Quincke,  "  Pogg.  Ann."  vol.  135,  p.  661. 

i  It  will  be  observed  that  the  value  here  given  on  the  authority  of  Quincke  is  much  higher  than  his  subsequent 
measurements,  as  quoted  above,  give. 

I  "  Proc.  Roy.  Soc."  1877,  and  "  Phil.  Trans.  Roy.  Soc."  1881,  1883,  and  1893. 

NOTE.  —  Quincke  points  out  that  substances  may  be  divided  into  groups  in  each  of  which  the  ratio  of  the  surface 
tension  to  the  density  is  nearly  constant.  Thus,  if  this  ratio  for  mercurv  be  taken  as  unit,  the  ratio  for  the  bromides 
and  iodides  is  about  a  half  :  that  of  the  nitrates,  chlorides,  sugars,  and  fats,  as  well  as  the  metals,  lead,  bismuth,  and 
antimony,  about  i ;  that  of  water,  the  carbonates,  sulphates,  and  probably  phosphates,  and  the  metals  platinum,  gold, 
silver,  cadmium,  tin,  and  copper,  2 ;  that  of  zinc,  iron,  and  palladium,  3 ;  and  that  of  sodium,  6. 

SMITHSONIAN  TABLES. 


144 


TABLE  1 3O. 
VAPOR    PRESSURES, 


The  vapor  pressures  here  tabulated  have  been  taken,  with  one  exception,  from  Regnault's  results. 
The  vapor  pressure  of  Pictet's  fluid  is  given  on  his  own  authority.  The  pressures  are  in  centimetres  ol 
mercury. 


Tem- 
pera- 
ture 
Cent. 

Acetone. 
C8H60 

Benzol. 
C6Ha 

Carbon 
bisul- 

"ST 

Carbon 
tetra- 
chloride. 

ecu 

Chloro- 
form. 
CHC18 

Ethyl 
alcohol. 
C2H60 

Ethyl 
ether. 
C4H100 

Ethyl 
bromide. 
C2H6Br 

Methyl 
alcohol. 
CH4O 

Turpen 
tine. 
CioH6 

—25° 

_ 

_ 

_ 

_ 

_ 

_ 

_ 

4.41 

.41 

_ 

—  20 
—  J5 

_ 

$8 

fil 

.98 

'•35 

— 

•33 
•5i 

6.89 
8-93 

IT, 

•63 

•93 

_ 

—10 

— 

1.29 

7-94 

1.85 

— 

.65 

11.47 

10.15 

J-35 

— 

—5 

*• 

1.83 

10.13 

2.48 

- 

.91 

14.61 

13.06 

1.92 

- 

0 

- 

2-53 

12.79 

3-29 

5^97 

1.27 

18.44 

16.56 

2.68 

.21 

5 

10 

_ 

3-42 
4-52 

1  6.00 
19.85 

4-32 
5.60 

10.05 

1.76 

2.42 

20.72 
25-74 

3-69 
5-oi 

.29 

15 

20 

17.96 

5.89 
7-56 

29.80 

7.17 
9.10 

16.05 

3-30 
4-45 

35-36 
43.28 

31.69 
38.70 

6.71 

8.87 

44 

25 

22.63 

9-59 

36.11 

"43 

20.02 

5-94 

52-59 

46.91 

1  1.  60 

_ 

30 

28.10 

12.02 

43-46 

14.23 

24-75 

7-85 

56.45 

15.00 

.69 

35 

34.52 

14.93 

51-97 

17-55 

30-35 

10.29 

76.12 

67.49 

19.20 

40 

42.01 

18.36 

6i-75 

21.48 

36.93 

13-37 

90.70 

80.19 

24-35 

1.08 

45 

50-75 

22.41 

72.95 

26.08 

44-00 

17.22 

107.42 

94-73 

30.61 

- 

50 

62.29 

27.14 

85-71 

3r-44 

53-50 

21.99 

126.48 

111.28 

38-17 

1.70 

55 

7J59 

32.64 

100.16 

37.63 

63-77 

27.86 

148.11 

130.03 

47.22 

60 

86.05 

39-01 

116.45 

44-74 

75-54 

35-02 

172.50 

151.19 

57-99 

2?65 

65 

101.43 

46.34 

134-75 

52.87 

88.97 

43-69 

199.89 

174-95 

70.73 

70 

118.94 

54-74 

155.21 

62.11 

104.21 

54-" 

230.49 

201.51 

85.71 

4.06 

75 

13876 

64.32 

177.99 

72.57 

121.42 

66.55 

264.54 

231.07 

103.21 

_ 

80 

85 

161.10 
186.18 

75.19 
87.46 

203.25 
231.17 

84.33 
97-51 

140.76 
162.41 

81.29 
98.64 

302.28 

343-95 

263.86 
300.06 

123.85 
147.09 

6.13 

90 

214.17 

101.27 

261.91 

112.23 

186.52 

118.93 

389-83 

339-89 

174.17 

9.06 

95 

245-28 

116.75 

296.63 

128.69 

213.28 

142.51 

440.18 

383-55 

205.17 

- 

100 

105 

279.73 
317.70 

134.01 
153.18 

332-51 
372.72 

146.71 
166.72 

242.85 
275.40 

169.75 
201.04 

495-33 

555-62 

431-23 
483.12 

240.51 
280.63 

13.11 

no 

359-40 

17444 

416.41 

188.74 

311.10 

236.76 

621.46 

539-40 

325-96 

18.60 

"5 

405.00 

197.82 

46374 

212.91 

350-10 

277-34 

693-33 

600.24 

376.98 

- 

120 

454.69 

223.54 

514.88 

239-37 

392.57 

323-17 

771.92 

665.80 

434.18 

25.70 

125 

508.62 

251.71 

569.97 

268.24 

438.66 

374.69 

_ 

736.22 

498.05 

_ 

130 

566.97 

282.43 

629.16 

299.69 

488.51 

432.3° 

— 

811.65 

569.13 

34-90 

135 

629.87 

315.85 

692.59 

333-86 

542.25 

496.42 

- 

892.19 

647-93 

140 

697.44 

352.07 

760.40 

370.90 

600.02 

567.46 

— 

977.96 

733-71 

46.40 

'45 

— 

391.21 

832.69 

411.00 

661.92 

645.80 

— 

830.89 

— 

150 

'55 

- 

433-37 
478.65 

909.59 

454-31 
501.02 

728.06 
798.53 

731-84 
825.92 

_ 

_ 

936.I3 

60.50 
68.60 

160 
165 

_ 

527-14 
568.30 

_ 

55i-3i 
605.38 

873.42 
952.78 

I 

I 

_ 

_ 

77-5° 

170 

634.07 

I 

663.44 

" 

" 

" 

" 

SMITHSONIAN  TABLES. 


TABLE  1 30  (continued). 
VAPOR    PRESSURES. 


145 


Tem- 
pera- 
ture, 
Centi- 
grade. 

Ammonia. 
NH3 

Carbon 
dioxide. 
C03 

Ethyl 
chloride. 
C2H5C1 

Ethyl 
iodide. 
C2H6I 

Methyl 
chloride. 
CH3C1 

Methylic 
ether. 
C2H60 

Nitrous 
oxide. 
N20 

Pictet's 
fluid. 
64SCM- 
44C02"by 
weight 

Sulphur 
dioxide. 
S02 

Hydrogen 
sulphide. 
H2S 

—30° 

86.61 

- 

1  1.  02 

- 

57-9° 

57-65 

- 

58.52 

28.75 

- 

—25 

110.43 

1300.70 

14.50 

_ 

71.78 

7I.6l 

1569.49 

67.64 

37.38 

374.93 

—  20 
—  !5 

139.21 

J73-65 

1514.24 

1758.25 

18.75 
23.96 

_ 

88.32 
107.92 

88.20 
107.77 

1758.66 
1968.43 

7448 
89.68 

47-95 
60.79 

443-85 

5J9-65 

—  IO 

214.46 

2034.02 

30.21 

— 

130.96 

130.66 

22OO.8O 

101.84 

76.25 

608.46 

—5 

264.42 

2344-I3 

37-67 

- 

157.87 

157-25 

2457.92 

121.60 

94-69 

706.60 

°s 

10 

15 

20 

3i8.33 
383-03 
457-40 

$$ 

2690.66 
3075-38 
3499-86 
3964.69 
4471.66 

46.52 

56.93 
OI.I1 

83.26 
99.62 

4.19 

5-4i 
6.92 
8.76 

II.OO 

189.10 
225.11 
266.38 

3!3-4i 
366.69 

187.90 
222.90 
262.90 
307.98 
358.60 

2742.10 
3055-86 
3401.91 

3783-I7 
4202.79 

139.08 

167.20 

193.80 
226.48 
258.40 

116.51 
142.11 

I7L95 
206.49 
246.20 

820.63 
949-08 
1089.63 
1244.79 
1415-15 

25 

747.70 

5020.73 

118.42 

13.69 

426.74 

415.10 

4664.14 

297.92 

291.60 

1601.24 

30 

870.10 

5611.90 

139.90 

16.91 

494.05 

477.80 

5170.85 

338.20 

343-i8 

1803.53 

35 

1007.02 

6244.73 

164.32 

20.71 

569.11 

— 

6335.98 

383.80 

401.48 

2002.43 

40 

"59-53 

6918.44 

191.96 

25-17 

- 

434.72 

467.02 

2258.25 

45 

1328.73 

7631.46 

223.07 

30.38 

— 

— 

- 

478.80 

540-35 

249543 

50 

1515-83 

- 

257-94 

36.40 

- 

- 

_ 

52I-36 

622.00 

2781.48 

55 

1721.98 

- 

266.84 

43-32 

- 

- 

- 

712.50 

3069.07 

60 

1948.21 

— 

340.05 

51.22 

— 

— 

— 

— 

812.38 

3374-02 

65 

2196.51 

- 

387.85 

- 

- 

- 

- 

922.14 

3696.15 

70 

2467-55 

~ 

440.50 

— 

— 

— 

— 

- 

- 

4035-32 

75 

2763.00 

- 

498.27 

_ 

_ 

_ 

_ 

_ 

_ 

_ 

80 

3084.31 

- 

561.41 

- 

- 

- 

- 

_ 

_ 

_ 

85 

3433-09 

— 

630.16 

— 

— 

— 

— 

_ 

_ 

_ 

90 

3810.92 

— 

704.75 

— 

— 

— 

— 

_ 

_ 

_ 

95 

4219.57 

— 

785.39 

— 

— 

- 

- 

- 

- 

- 

100 

4660.82 

- 

872.28 

- 

- 

- 

- 

- 

- 

- 

SMITHSONIAN  TABLES. 


146 


TABLES  131-132. 
VAPOR   PRESSURE. 


TABLE  131.  —Vapor  Pressure  of  Ethyl  Alcohol.* 


u 

d 
§ 

H 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

Vapor  pressure  in  millimetres  of  mercury  at  o°  C. 

0° 

10 

20 
30 

40 

g 

70 

12.24 

23.78 
44-00 
78.06 

I33-70 
220.00 

350-30 
541.20 

13.18 

2S-31 
46.66 
82.50 

H0.75 
230.80 
366.40 
564-35 

14.15 
27.94 

49-47 
87.17 

148.10 
242.50 
3^3-10 
588.35 

15.16 

28.67 

52-44 
92.07 

I55-80 
253.80 
400.40 
613.20 

16.21 

30-5° 
55-56 
97-21 

163.80 
265.90 
4i8.35 
638-95 

I7-3I 

32-44 
58.86 
102.60 

172.20 
278.60 
437-oo 
665.55 

18.46 
34-49 
62.33 
108.24 

181.00 
291.85 

456.35 
693.10 

19.68 
36-67 
65-97 
114.15 

190.10 
305.65 
476.45 
721.55 

20.98 

120.35 

199.65 
3  *  9-95 
497-25 
751.00 

22.34 
41.40 

73-83 
126.86 

209.60 

334-85 
518.85 

781.45 

From  the  formula  log/  =  a  -f-  ba?  -\-  cf?  Ramsay  and  Young  obtain  the  following  numbers.t 

0 

£ 

0° 

10° 

20° 

30° 

40° 

50° 

60° 

70° 

80° 

90° 

Vapor  pressure  in  millimetres  of  mercury  at  o°  C. 

0° 

IOO 
200 

12.24 
1692.3 
22182. 

23-73 
2359-8 
26825. 

43-97 
3223-0 
32196. 

78.11 
43l8-7 
38389- 

I33-42 
5686.6 
455I9- 

219.82 
7368.7 

350-21 
9409.9 

540.91 
11858. 

811.81 
14764. 

1186.5 
18185. 

TABLE  132.  — Vapor  Pressure  of  Methyl  Alcohol,  t 


u 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

0, 

I 

£ 

Vapor  pressure  in  millimetres  of  mercury  at  o°  C. 

0° 

IO 

Sf 

31.6 

57-o 

33-6 
60.3 

35-6 
63.8 

37-8 

67-5 

40.2 
71.4 

42.6 

75-5 

45-2 
79-8 

47-9 
84-3 

50.8 
89.0 

20 

94-o 

99-2 

104.7 

110.4 

116.5 

122.7 

129.3 

136.2 

143-4 

151.0 

30 

158.9 

167.1 

175-7 

184.7 

194.1 

203.9 

214.1 

224.7 

235-8 

247.4 

40 

259.4 

271.9 

285.0 

298.5 

312.6 

327-3 

342.5 

358.3 

374-7 

391-7 

£ 

4094 
624.3 

427.7 
650.0 

446.6 
676.5 

466.3 
703.8 

486.6 
732.0 

507-7 

76!.I 

529-5 
791.1 

552-o 
822.0 

575-3 

599-4 

*  This  table  has  been  compiled  from  results  published  by  Ramsay  and  Young  (Jour.  Chem.  Soc.  vol.  47,  and  Phil. 
Trans.  Roy.  Soc.,  1886). 

t  In  this  formula  01  —  5.0720301;   log  b=.  2". 6406 13 1 ;  log  c  —  0.6050854 ;  log  a  =r  0.003377538;  log  /3  — 1.99682424 
(c  is  negative). 

%  Taken  from  a  paper  by  Dittmar  and  Fawsitt  (Trans.  Roy.  Soc.  Edin.  vol.  33). 
SMITHSONIAN  TABLES. 


TABLE  133. 
VAPOR  PRESSURE.* 

Carbon  Bisulphide,  Cnlorobenzene,  Bromofcenzene,  and  Aniline. 


147 


Temp. 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

(a)  CARBON  BISULPHIDE. 

0° 

127.90 

I33-85 

140.05 

146.45 

153.10 

160.00 

167.15 

174.60 

182.25 

190.20 

10 
20 
30 
40 

198.45 
298.05 
434.60 
617.50 

207.00 
309.90 
450-65 
638.70 

215.80 
322.10 

467-15 
660.50 

224.95 
334-70 
484.15 
682.90 

234.40 
347-70 
501.65 
705.90 

244.15 
361.10 

5  i  9-65 
729.50 

374-95 
538.15 
753-75 

264.65 
389.20 

557-15 
778.60 

275.40 
403.90 

576.75 
804.10 

286.55 
419.00 
596.85 
830.25 

(b)  CHLOROBENZENE. 

20° 

8.65 

9.14 

9.66 

10.21 

10.79 

11.40 

12.04 

12.71 

13.42 

14.17 

30 
40 

r4-95 
25.10 

15-77 
26.38 

16.63 

27.72 

17-53 
29.12 

18.47 
30.58 

1945 
32.10 

20.48 
33-69 

21.56 

35-35 

22.69 
37.o8 

38^88 

50 

60 

40.75 
64.20 

42.69 
67.06 

44-72 
70.03 

46.84 

73-n 

49-05 
76.30 

51-35 
79.60 

53-74 
83.02 

56.22 
86.56 

58.79 
90.22 

61.45 
94.00 

80 

97.90 
144.80 

101.95 
150.30 

106.10 
156.05 

110.41 
161.95 

114.85 
168.00 

"9-45 
174-25 

124.20 
181.70 

129.10 
187.30 

134.15 
194.10 

139.40 
201.15 

90 

208.35 

215.80 

22345 

231.30 

239-35 

247.70 

256.20 

265.00 

274.00 

283.25 

100 

292-75 

302.50 

312.50 

322.80 

333-35 

344.15 

355-25 

366.65 

378.30 

390-25 

no 

120 

130 

402.55 
542.80 
718.95 

415.10 
558-70 
738.65 

427-95 
575-05 
758.80 

441-15 
S9I-7Q 

454.65 
608.75 

468.50 
626.15 

482.65 
643-95 

497-20 
662.15 

512.05 
680.75 

699.65 

(c)  BROMOBENZENE. 

40° 

- 

- 

- 

- 

- 

12.40 

13.06 

13-75 

14.47 

15.22 

50 

1  6.00 

16.82 

17.68 

18.58 

19.52 

20.50 

21.52 

22.59 

23-71 

24.88 

60 

26.10 

27.36 

28.68 

30.06 

3I-50 

33-oo 

34-56 

36.18 

39-60 

1° 
80 

41.40 
63.90 

£3 

45-24 
69.48 

47.28 
7242 

49.40 
75-46 

51.60 
78.60 

53-88 
81.84 

56-25 
85.20 

88^68 

61.26 
92.28 

90 

96.00 

99-84 

103.80 

107.88 

112.08 

116.40 

120.86 

125.46 

130.20 

135-08 

100 

IIO 

140.10 
198.70 

145.26 
205.48 

150.57 
212.44 

156-03 
219.58 

161.64 
226.90 

167.40 
234.40 

I73-32 
242.10 

179.41 
250.00 

183.67 
258.10 

192.10 
266.40 

1  20 

274.90 

283.65 

292.60 

3OI-75 

311.15 

320.80 

330.70 

340.80 

35I-I5 

361.80 

130 

372-65 

383.75 

395-  I0 

406.70 

418.60 

430-75 

443-20 

455-90 

468.90 

482.20 

140 

495.80 

509.70 

523.90 

538-40 

553-20 

568.35 

599-65 

632.25 

150 

649.05 

666.25 

683.80 

701.65 

7I9-95 

738.55 

757-55 

776.95 

796.70 

816.90 

(d)  ANILINE. 

80° 

18.80 

19.78 

20.79 

21.83 

22.90 

24.00 

25.14 

26.32 

27-54 

28.80 

90 

30.10 

31-44 

32.83 

34.27 

35-76 

37.30 

38-90 

40-56 

42.28 

44-06 

100 

IIO 

45-90 
68.50 

47-80 
71.22 

49.78 
74.04 

51.84 
76.96 

53-98 
79-98 

56.20 
83.10 

58.50 
86.32 

60.88 
89.66 

63-34 
93.12 

65.88 
96.70 

1  20 

100.40 

104.22 

108.17 

112.25 

116.46 

120.80 

125.28 

129.91 

134.69 

139.62 

130 

144.70 

149.94 

155-34 

160.90 

166.62 

172.50 

178.56 

184.80 

191.22 

197.82 

140 

204.60 

211.58 

218.76 

226.14 

233-72 

241.50 

249.50 

257.72 

266.16 

274.82 

150 

160 

283.70 
386.00 

292.80 
397-65 

302.15 
409.60 

3"-75 
421.80 

321.60 
434-30 

33I-70 
447.10 

342.05 
460.20 

352.65 
473-60 

363-50 
487.25 

374.60 
501.25 

170 

5I5-6o 

530.20 

545-20 

560.45 

576.10 

592.05 

608.35 

625.05 

642.05 

659-45 

1  80 

677.15 

695-30 

7I3-75 

732.65 

75I-90 

771.5° 

" 

*  These  tables  of  vapor  pressures  are  quoted  from  results  published  by  Ramsay  and  Young  (Jour.  Chem.  Soc. 
vol.  47).    The  tables  are  intended  to  give  a  series  suitable  for  hot-jacket  purposes. 
SMITHSONIAN  TABLES. 


148 


TABLE  133  (continued). 
VAPOR  PRESSURE. 

Methyl  Salicylate,  Bromonaphtlialine,  and  Mercury. 


Temp. 
C. 

0° 

1° 

2° 

3° 

40 

6° 

6° 

7° 

8° 

9° 

(e)  METHYL  SALICYLATE. 

70° 

2.40 

2.38 

2.77 

2.97 

3-i8 

3-40 

3.62 

3-85 

4.09 

4-34 

80 

4.60 

4.87 

3'15 

5-44 

5-74 

6.05 

6-37 

6.70 

7-05 

7.42 

90 

7.80 

8.20 

8.62 

9.06 

9-52 

9-95 

10.44 

10.95 

11.48 

12.03 

100 

12.60 

13.20 

13.82 

14.47 

^S 

15-85 

16.58 

17-34 

18.13 

18.95 

no 

19.80 

20.68 

21.60 

22.55 

23-53 

24-55 

25.61 

26.71 

27.85 

29.03 

120 

30-25 

31-52 

32-84 

34-21 

35-63 

37.10 

38.67 

40.24 

41.84 

43-54 

130 

45-3° 

47.12 

49.01 

50-96 

52-97 

55-05 

57.20 

59-43 

61-73 

64.10 

140 

66.55 

69.08 

71.69 

74.38 

77-15 

80.00 

82.94 

85-97 

89.09 

92.30 

150 

95.60 

99.00 

102.50 

106.10 

109.80 

113.60 

H7-51 

I2i-53 

125.66 

129.90 

160 
170 

134-25 
184.70 

138.72 
190.48 

I43.3I 
196.41 

148.03 
202.49 

152.88 
208.72 

157-85 
215.10 

162.95 
221.65 

168.19 
228.30 

I73-56 
235-I5 

179.06 
242.15 

180 
190 

249-35 
330-85 

256.70 
340.05 

264.20 
349-45 

271.90 
359.05 

279-75 
368.85 

287.80 
378-90 

296.00 

304.48 
399-6o 

3'3-05 
410.30 

321-85 
421.20 

200 

432.35 

443-75 

4^5-35 

467.25 

479-35 

491.70 

504.35 

5I7-25 

530.40 

543-So 

2IO 

557-50 

571-45 

585-70 

600.25 

615-05 

630.15 

645-55 

661.25 

677-25 

693.60 

2  2O 

710.10 

727.05 

744-35 

761.90 

779-85 

798.10 

(f)  BROMONAPHTHALINE. 

110° 

3-6o 

3-74 

3-89 

4.05 

4.22 

4.40 

4-59 

4-79 

5-oo 

5.22 

1  20 

130 

5-45 
8.50 

5-70 
8.89 

5.96 
9-29 

6.23 
9.71 

6.51 
10.15 

6.80 
1  0.60 

7.10 
11.07 

7.42 
11.56 

7.76 
12.07 

8.12 

12.60 

140 

I3-I5 

I3-72 

I4-31 

14.92 

15-55 

16.20 

16.87 

17-56 

18.28 

19.03 

150 

160 

19.80 
28.85 

20.59 
29.90 

21.41 
30.98 

22.25 
32-09 

23.11 

33-23 

24.00 
34-40 

24.92 
35-6o 

25.86 
36-83 

26.83 
38.10 

27-83 
39-4i 

170 

40-75 

42.12 

43-53 

44-99 

46.50 

48.05 

49.64 

51.28 

52-96 

54-68 

180 

56.45 

58-27 

60.14 

62.04 

64.06 

66.10 

68.19 

70-34 

72-55 

74.82 

190 

77.15 

79-54 

81.99 

84.51 

87.10 

89.75 

92.47 

95.26 

98.12 

101.05 

200 

104.05 

107.12 

110.27 

H3-50 

116.81 

120.20 

123.67 

127.22 

130.86 

W59 

210 
22O 

138.40 
181.75 

142.30 
186.65 

146.29 
191.65 

150-38 
1  96-7  5 

J54-57 
202.00 

158.85 
207.35 

163-25 
212.80 

167.70 
218.40 

172.30 
224.15 

176.95 
230.00 

230 

235-95 

242.05 

248.30 

254-65 

261.20 

267.85 

274.65 

281.60 

288.70 

295-95 

240 

303.35 

310.90 

318.65 

326.50 

334-55 

342-75 

351-10 

359-65 

368.40 

377-3° 

250 

386.35 

395-6o 

405-05 

414.65 

42445 

434-45 

444-65 

455-00 

465.60 

476.35 

260 

487-35 

498.55 

509.90 

521-50 

533-35 

545-35 

557-60 

570.05 

582.70 

595.60 

270 

608.75 

622.10 

635-70 

649-5° 

663-55 

677-85 

692.40 

707-15 

722.15 

737-45 

(g)  MERCURY. 

270° 

123.92 

126.97 

130.08 

133.26 

136.5° 

139.81 

143.18 

146.61 

150.12 

15370 

280 

157-35 

161.07 

164.86 

168.73 

172.67 

176.79 

180.88 

185.05 

189.30 

1  93-63 

290 

198.04 

202.53 

207.10 

211.76 

216.50 

221.33 

226.25 

231.25 

236.34 

241-53 

300 

246.81 

252.18 

257-65 

263.21 

268.87 

274-63 

280.48 

286.43 

292.49 

298.66 

310 

304.93 

311-30 

317-78 

324-37 

33i.o8 

337.89 

344.81 

35I-85 

359.00 

366.28 

320 

373-67 

381.18 

388.81 

396-56 

404.43 

412.44 

420.58 

428.83 

437.22 

445-75 

330 
340 

454-41 
548.64 

463.20 
558.87 

472.12 
569-25 

481.19 
57978 

490.40 
590-48 

499-74 
601.33 

509.22 
612.34 

518.85 
623.51 

528.63 
634.85 

I3?'56; 
646.36 

350 

658.03 

669.86 

681.86 

694.04 

706.40 

718.94 

731-65 

744-54 

757.6i 

770.87 

360 

784-3! 

SMITHSONIAN  TABLES. 


TABLE  134.  149 

VAPOR  PRESSURE  OF  SOLUTIONS  OF  SALTS  IN  WATER.* 

The  first  column  gives  the  chemical  formula  of  the  salt.  The  headings  of  the  other  columns  give  the  number  of 
gramme-molecules  of  the  salt  in  a  litre  of  water.  The  numbers  in  these  columns  give  the  lowering  of  the 
vapor  pressure  produced  by  the  salt  at  the  temperature  of  boiling  water  under  76  centimetres  barometric  pressure. 


Substance. 

0.5 

1.0 

2.0 

3.0 

4.0 

5.0 

6.0 

8.0 

10.0 

A12(S04)3    .        .        . 
A1C13  .... 

12.8 

22.5 

36.5 

61.0 

179.0 

318.0 

Ba(S03)2     .        .        . 

6.6 

154 

344 

Ba(OH)2     . 

12.3 

22.5 

Ba(NO3)2    . 

27.0 

Ba(ClO3)2    . 
BaCl2  .... 

15.8 
16.4 

33-3 
36-7 

70.5 
77.6 

1  08.2 

BaBr2  .         ... 

1  6.8 

38.8 

91.4 

150.0 

204.7 

Ca(S03)2     .        .       .. 

9-9 

23.0 

56.0 

1  06.0 

Ca(N03)2    .     ;.-      ;,: 

16.4 

34-8 

74.6 

139-3 

161.7 

205.4 

CaCl2  .... 

17.0 

39-8 

95-3 

166.6 

241.5 

3I9-5 

CaBr2  .... 

17.7 

44.2 

105.8 

191.0 

283.3 

368.5 

CdSO4 

4-1 

o.Q 

18.1 

CdI2    .... 

7-6 

14.8 

33-5 

52-7 

CdBr2. 

8.6 

17.8 

f\ 

55-7 

8o.O 

CdCl2. 

9.6 

18.8 

36-7 

57-0 

77-3 

99-o 

Cd(NO3)2   . 

36.1 

78.0 

122.2 

Cd(ClO3)2  . 

17-5 

CoSO4 

5-5 

10.7 

22.9 

45-5 

CoCl2. 

15.0 

34-8 

83.0 

136.0 

186.4 

Co(N03)2    .        .        . 

17-3 

39-2 

89.0 

152.0 

218.7 

282.0 

332.0 

FeS04 

5-8 

10.7 

24.0 

42.4 

H3B03 
H3P04         .         .         . 

6.0 
6.6 

12.3 
14.0 

25.1 
28.6 

38.0 
45-2 

62.0 

81.5 

103.0 

146.9 

189.5 

H3AsO4 

7-3 

15.0 

30.2 

46.4 

64.9 

H2S04 

12.9 

26.5 

62.8 

104.0 

148.0 

198.4 

247.0 

343-2 

KH2PO4     . 

10.2 

33-3 

47-8 

60.5 

73-i 

85.2 

KN03. 
KC1O3 

10.6 

21.  1 
21.6 

40.1 
42.8 

57-6 
62.1 

74-5 
80.0 

88.2 

IO2.I 

126.3 

148.0 

KBrO3 

10.9 

22.4 

45-o 

KHSO4       . 

10.9 

21-9 

43-3 

65-3 

85.5 

107.8 

129.2 

170.0 

KNO2 

ii.  i 

22.8 

44-8 

67.0 

90.0 

110.5 

I30-7 

167.0 

198.8 

KC1O4 

"•5 

22.3 

KC1     .... 

12.2 

24.4 

48.8 

74.1 

100.9 

128.5 

152.2 

KHC02      . 

II.6 

23-6 

59-o 

77-6 

104.2 

132.0 

1  60.0 

2IO.O 

255.0 

KI       . 
K2C2O4 

12-5 

25-3 
28.3 

52-2 
59-8 

82.6 
94-2 

1  1  2.2 
I3I.O 

141-5 

I7I.8 

225-5 

278.5 

K2W04       . 

!3-9 

33-o 

75-o 

123.8 

1754 

226.4 

K2CO3 
KOH  .... 

14.4 

31.0 

29-5 

68.3 
64.0 

105-5 
99-2 

I52.O 
I4O.O 

209.0 
181.8 

258.5 
223.0 

350-0 
309.5 

387.8 

K2Cr04       . 

16.2 

29-5 

60.0 

LiNO3 

12.2 

25-9 

55-7 

88.9 

122.2 

I55-I 

188.0 

2534 

309.2 

LiCl     .... 
LiBr    .... 

I2.I 
12.2 

25-5 
26.2 

57-i 
60.0 

97-o 

!32-5 

140.0 

175-5 
186.3 

219.5 
241.5 

34r-5 

393.5 
438.0 

Li2SO4 

13-3 

28.1 

56.8 

89.0 

LiHSO4      . 
Lil       . 

Li2SiFl6       . 

12.8 
I3.6 
154 

27.0 
28.6 
34-0 

64.7 
70.0 

93-o 

105.2 
1  06.0 

130.0 

154.5 

168.0 
206.0 

264.0 

357-0 

445-0 

LiOH  .... 
Li2CrO4       . 

15.9 
16.4 

374 
32.6 

78.1 
74-o 

120.0 

171.0 

*  Compiled  from  a  table  by  Tammann,  "  MeSm.  Ac.  St.  Petersb."  35,  No.  9,  1887.     See  also  Referate,  "Zeit.  f. 
Phys."  ch.  2,  42,  1886. 

SMITHSONIAN  TABLES. 


I5O  TABLE  1  34  (continued). 

VAPOR   PRESSURE   OF  SOLUTIONS  OF  SALTS    IN   WATER. 


Substance. 

0.5 

1.0 

2.0 

3.0 

4.0 

6.0 

6.0 

8.0 

10.0 

MgS04        .        .        . 
MgCl2.        .        .        . 

i6J 

12.0 
39-0 

24-5 
100.5 

47-5 
183-3 

277.0 

377-0 

Mg(N03)2  .        .        . 

17.6 

42.0 

IOI.O 

174.8 

MgBr2 

17.9 

44-o 

115.8 

205.3 

298.5 

MgH2(S04)2       .        . 

18.3 

46.0 

1  1  6.0 

MnSO4 

6.0 

10.5 

2I.O 

MnCl2.        .        . 

15.0 

34-0 

76.0 

122.3 

167.0 

209.0 

NaH2PO4    . 

10.5 

20.0 

36.5 

66.8 

82.0 

96.5 

126.7 

157-1 

NaHSO4     . 
NaNO3 

10.9 
10.6 

22.1 

22-5 

47.3 

46.2 

Iff 

IOO.2 
90-3 

126.1 
111.5 

148.5 

189.7 
167.8 

231.4 
198.8 

NaClO3       . 

10.5 

23.0 

48.4 

73-5 

98.5 

123-3 

147.5 

196.5 

223.5 

(NaP03)6    . 

n.6 

NaOH 

1  1.8 

22.8 

48.2 

77-3 

107-5 

I39-1 

172.5 

243-3 

314.0 

1  NaNO2 

1  1.6 

24.4 

50.0 

75-o 

98.2 

122.5 

146.5 

189.0 

226.2 

NaHPO4     . 

I2.I 

23-5 

43.0 

60.0 

78.7 

99-8 

122.  1 

NaHCO2    .        . 

I2.9 

24.1 

48.2 

77-6 

102.2 

127.8 

152.0 

198.0 

239.4 

NaSO4 

12.6 

25.0 

48.9 

74-2 

NaCl   .... 

I2.3 

25.2 

52.1 

80.0 

III.O 

143.0 

176.5 

NaBrO3       . 

12.  1 

25.0 

54-i 

81.3 

108.8 

136.0 

NaBr  .... 

12.6 

25'9 

57-0 

89.2 

124.2 

159-5 

197.5 

268.0 

Nal      . 

I2.I 

25.6 

60.2 

99-5 

136.7 

177-5 

221.0 

301-5 

370.0 

Na4P2O7      . 

13.2 

22.0 

Na2CO3 

14.3 

27.3 

53-5 

80.2 

III.O 

Na2C2O4      . 
Na2WO4     . 

14-5 
14.8 

30.0 

33-6 

71.6 

105.8 
"5'7 

146.0 
162.6 

Na3P04       . 

16.5 

30.0 

52-5 

(NaP03)3    .        .        . 

17.1 

36.5 

NH4NO3     . 

12.8 

22.O 

42.1 

62.7 

82.9 

103.8 

I2I.O 

152.2 

1  80.0 

(NH4)2SiFl6 

"•5 

25.0 

44-5 

NH4C1 

I2.O 

23-7 

69-3 

94.2 

118.5 

138.2 

179.0 

213.8 

NH4HS04  . 

"•5 

22.0 

46.8 

71.0 

94-5 

118. 

139.0 

181.2 

218.0 

(NH4)2S04.        .        . 

1  1.0 

24.0 

46.5 

93-o 

117.0 

I4I.8 

NH4Br 

11.9 

23.9 

48.8 

74.1 

99-4 

121.5 

145-5 

190.2 

228.5 

NH4I  .... 

12.9 

25.1 

49.8 

78.5 

104.5 

132-3 

156.0 

200.0 

243-5 

NiSO4          ... 

5-0 

10.2 

21.5 

NiCl2  .... 

16.1 

37-o 

86.7 

147.0 

212.8 

Ni(N03)2     .        .        . 

16.1 

37-3 

91.3 

156.2 

235.0 

Pb(NO3)2    . 

12.3 

23-5 

45-o 

63.0 

Sr(S03)2      .        .         . 

7.2 

20.3 

47.0 

Sr(N03)2     . 

15.8 

31.0 

64.0 

974 

I3M 

SrCl2  .... 

16.8 

38.8 

91.4 

156.8 

223.3 

281.5 

SrBr2  .... 

17.8 

42.0 

IOI.I 

179.0 

267.0 

ZnS04 

4-9 

10.4 

21.5 

42.1 

66.2 

ZnCl2  .... 

9.2 

18.7 

46.2 

75>o 

107.0 

I53-° 

195.0 

Zn(N03)2     .         .         . 

16.6 

39-o 

93-5 

157-5 

223.8 

SMITHSONIAN  TABLES. 


TABLE  135.  I$I 

PRESSURE   OF   AQUEOUS   VAPOR   AT   LOW   TEMPERATURE.* 

Pressures  are  given  in  inches  and  millimetres  of  mercury,  temperatures  in  degrees  Fahrenheit  and  degrees  Centigrade. 


(a)  Pressures  in  inches  of  mercury  ;  temperatures  in  degrees  Fahrenheit. 

Temp.  F. 

o°.o 

1°.0 

2°.0 

3°.0 

4°.0 

5°.0 

6°.0 

7°.0 

8°.0 

9°.0 

—50° 

—40 

—3° 
—  20 

—  10 

—0 

+o 

10 
20 

3° 

0.0021 

.0039 
.0069 
.0126 

.0222 

0.0383 

.0383 
.0631 
.1026 
.1641 

0.0019 
.0037 
.0065 
.0119 

.0210 

0.0263 
.0403 
.0665 
.1077 
.1718 

0.0018 
•0035 
.0061 

.OI  1  2 
.0199 

0.0244 
.0423 
.0699 
.II3O 
.1798 

0.0017 
•0033 
.0057 
.0106 
.0188 

0.0225 
.0444 

•0735 
.1185 

0.0016 
.0031 
.0054 

.0100 

.0178 

0.0307 
.0467 
.0772 
.1242 

0.0015 
.0029 
.0051 
.0094 
.0168 

0.0291 
.0491 
.0810 
.1302 

0.0013 
.0027 
.0048 
.0089 
.0159 

0.0275 

•0515 
.0850 

•1365 

0.0013 
.0026 
.0046 
.0083 
.0150 

0.0260 
.0542 
.0891 
.1430 

O.OOI2 
.0024 
.0044 
.0078 
.0141 

O.0247 
.0570 

•0933 
.1497 

O.OOII 

.0022 
.0041 

.0074 
•0133 

0.0234 
.0600 

.0979 
.1568 

(V)  Pressures  in  millimetres  of  mercury  ;  temperatures  in  degrees  Fahrenheit. 

Temp.  F. 

o°.o 

1°.0 

2°.0 

3°.0 

4°.0 

5°.0 

6°.0 

7°.0 

8°.0 

9°.0 

—50° 

—40 

—30 
—  20 

—  10 

—0° 

+o 

10 

20 
3° 

0.053 

.100 

.176 
.319 
•564 

0.972 
.972 
1.603 
2.607 
4.169 

0.049 
.094 
.165 
.301 
•534 

0.922 
1.023 
1.688 
2-735 
4-364 

0.046 
.089 

'III 

•505 

0.873 

1-075 
1.776 
2.869 
4.568 

0.043 
.084 
.146 
.268 
478 

0.826 
1.129 
1.867 
3.009 

0.040 
.079 
.138 

•253 

.452 

0.781 
1.186 
1.961 
3-155 

0.037 
.074 
.130 

•239 

.427 

0.738 
1.246 
2.058 
3.307 

0.034 
.069 
.123 
.225 
.403 

0.698 

2.158 
3.466 

0.032 
.065 
.117 

.212 
.384 

0.661 
1.376 
2.262 
3-631 

0.030 
.001 
.in 

0.627 

1.447 
2.371 
3-803 

0.028 

•057 
.105 
.187 
•338 

0-595 
1.523 

3-982 

(C)  Pressures  in  inches  of  mercury  ;  temperatures  in  degrees  Centigrade. 

Temp.  C. 

o°.o 

1°.0 

2°.0 

3°.0 

4°.0 

5°.0 

6°.0 

7°.0 

8°.0 

9°.0 

—0° 

—  10 
—  20 

—30 
—40 

0.1798 
.0772 
.0307 

.0112 

.0040 

0.1655 
.0706 
.0278 

.0101 

.0036 

0.1524 
.0645 
.0252 
.0091 
.0032 

0.1395 

.0229 
.0082 
.0029 

0.1290 

•°537 
.0208 
.0073 
.0025 

0.1185 
.0491 
.0188 
.0065 
.0022 

0.1091 
.0449 
.0171 
.0059 

.0020 

0.0998 
.0411 
•0153 
•0053 
.0017 

0.0916 

•0375 
•0138 
.0048 
.0015 

0.0842 
.0341 
.0124 
.0044 
.0013 

(d)  Pressures  in  millimetres  of  mercury  ;  temperatures  in  degrees  Centigrade. 

Temp.  C. 

o°.o 

1°.0 

2°0 

3°.0 

4°.0 

6°.0 

6°.0 

7°.0 

8°.0 

9°.0 

—0° 

—  10 
—  20 

—3° 
—40 

4.568 
1.961 
0.781 
0.284 

O.IOO 

4.208 
1.794 
0.706 
0.256 
0.090 

3-875 
1.637 
0.641 
0.231 
O.oSl 

3-565 
1-493 
0.583 
0.207 
0.072 

3-277 
I-363 
0.528 
0.185 
0.064 

3.009 
1.246 
0.478 
0.165 
0.057 

2.767 
1.140 
0.432 
0.148 
0.050 

2-534 
1.044 
0.389 

o.i33 
0.044 

2.327 
0.952 
0-350 

O.I2I 
0.039 

2.138 
0.864 
0.315 

O.I  10 

0.034 

*  Marvin's  results  (Ann.  Rept.  U.  S.  Chief  Signal  Officer,  1891,  App.  10). 
SMITHSONIAN  TABLES. 


152 


TABLE  136. 
PRESSURE  OF  AQUEOUS  VAPOR,  0°  C  TO  100°  C. 

According  to  Broch.* 


Temp. 
°C 

0.0 

0.2 

0.4 

0.6 

0.8 

1.0 

1.2 

1.4 

1.6 

1.8 

+o 

4.57 

4.64 

4-70 

477 

4-84 

4.91 

4.98 

5.05 

5-12 

5.20 

2 

I 

8 

5.27 

6.07 

6.97 
7.99 

5-35 
6.15 
7.07 
8.10 

5.42 
6.24 
7.17 

8.21 

5.50 
6-33 
7.26 
8.32 

5.58 
6.42 
7.36 
8.43 

5.66 
6.51 
7-47 
8-55 

5-74 
6.60 

7-57 
8.66 

^69 

7.67 
8.78 

5-90 
6.78 
7.78 
8.90 

9.02 

10 

9.14 

9.26 

9-39 

9-51 

9.64 

9-77 

9-90 

10.03 

10.16 

10.30 

12 

10.43 

10.57 

10.71 

40.85 

10.99 

11.14 

11.28 

"43 

11.58 

"•73 

14 

1  1.88 

12.04 

12.19 

12.35 

12.51 

12.67 

12.84 

13.00 

13.17 

J3-34 

16 

13.51 

13.68 

13-86 

14.04 

14.21 

14.40 

14.58 

14.76 

J4-95 

I5-M 

18 

15-33 

I5-52 

15.72 

15.92 

16.12 

16.32 

16.52 

16.73 

16.94 

17.15 

20 

17-36 

I7-58 

17.80 

18.02 

18.24 

18.47 

18.69 

18.92 

19.16 

19-39 

22 

19.63 

19.87 

20.11 

20.36 

20.61 

20.86 

21.  II 

21.37 

21.63 

21.89 

24 

22.15 

22.42 

22.69 

22.96 

23.24 

23-52 

23.80 

24.08 

24-37 

24.66 

26 

24.96 

25-25 

25-55 

25.86 

26.16 

26.47 

26.78 

27.10 

27.42 

27.74 

28 

28.07 

28.39 

28.73 

29.06 

29.40 

29-74 

30.09 

3°-44 

30-79 

30 

31.51 

31-87 

32.24 

32.61 

32.99 

33-37 

33-75 

34-14 

34-53 

34-92 

32 

35-32 

35-72 

36.13 

36-54 

36.95 

37-37 

37-79 

38.22 

38.65 

39-08 

34 

39-52 

39-97 

40.41 

40.87 

41.32 

41.78 

42.25 

42.72 

43.19 

43-67 

36 

44.16 

44-65 

45-M 

46.14 

46.65 

47.16 

47.68 

48.20 

48.73 

38 

49.26 

49.80 

50.34 

50.89 

5M4 

52.00 

52-56 

53-13 

53-70 

54.28 

40 

42 

54.87 
61.02 

55-46 
61.66 

56-05 
62.32 

56.65 
62.98 

57-26 
63.64 

57.87 
64.31 

58.49 
64.99 

59-11 
65.67 

59-74 
66.36 

60.38 
67.05 

44 

67-76 

68.47 

69.18 

69.90 

70.63 

7I-36 

72.10 

72.85 

73-6o 

74.36 

46 

75.13 

75-91 

76.69 

77-47 

78.27 

79.07 

79.88 

80.70 

81.52 

82.35 

48 

83.19 

84.03 

84.89 

85-75 

86.61 

87.49 

88.37 

89.26 

90.16 

91.06 

50 

91.98 

92.90 

93-83 

94-77 

95.7i 

96.66 

97-63 

98.60 

99-57 

100.56 

52 

101.55 

102.56 

103-57 

104.59 

105.62 

106.65 

107.70 

108.76 

109.82 

110.89 

54 

111.97 

113.06 

114.16 

115.27 

116.39 

117.52 

1  18.65 

119.80 

120.95 

122.12 

56 

123.29 

124.48 

125.67 

126.87 

128.09 

129.31 

130-54 

131.79 

I33-04 

134.30 

58 

I35-58 

136.86 

138.15 

139.46 

140.77 

142.10 

H3-43 

144.78 

146.14 

I47.5I 

60 

148.88 

150.27 

151.68 

I53-09 

I54-51 

155.95 

157.39 

158.85 

160.32 

161.80 

62 

163.29 

164.79 

166.31 

167.83 

169.37 

170.92 

172.49 

174-06 

I75-65 

177.25 

64 

178.86 

180.48 

182.12 

18377 

185-43 

187.10 

188.79 

190.49 

192.20 

1  93-93 

66 

I95-67 

197.42 

199.18 

200.96 

202.75 

204.56 

206.38 

208.21 

210.06 

211.92 

68 

213.79 

215.68 

217.58 

219.50 

221.43 

223-37 

225-33 

227.30 

229.29 

231-29 

70 

233.31 

235-34 

237.39 

239-45 

241.52 

243-62 

245-72 

247.85 

249.98 

252.14 

72 

254-3° 

256.49 

258.69 

260.91 

263.14 

265.38 

267.65 

269.93 

272.23 

274.54 

74 

276.87 

279.21 

281.58 

283-95 

286.35 

288.76 

291.19 

293.64 

296.11 

298.59 

76 

78 

301.09 
327.05 

303.60 
329.75 

306.14 
332.47 

335-20 

311.26 
337-95 

3^3-85 
340-73 

3l6-45 
343-52 

319.07 
346.33 

321.72 
349.16 

324-38 
352-01 

80 

354.87 

35776 

360.67 

363-59 

366.54 

369-51 

372.49 

375.50 

378.53 

381-58 

82 
84 

384.64 
416.47 

387-73 
4I9-77 

390.84 
423.09 

393-97 
426.44 

397-12 
429.81 

400.29 
433-  J  9 

403.49 
436.60 

406.70 
440.04 

409-94 
443-49 

446.97 

86 

4S0.47 

454.00 

457-54 

461.11 

464.71 

468.32 

471.96 

475-63 

479-32 

483-03 

88 

486.76 

490.52 

494.31 

498.12 

501.95 

505.81 

509.69 

5I7-53 

521.48 

90 

92 

525-47 
566.7  1 

529.48 
570.98 

533.51 
575.28 

537.57 
579.6i 

541-65 
583.96 

545-77 

549.90 
592-74 

554-07 
597-17 

558.26 
601.64 

562.47 
606.13 

94 

610.64 

615.19 

619.76 

624.37 

629.00 

633.66 

638.35 

643.06 

647.81 

652-59 

96 

657.40 

662.23 

667.10 

672.00 

676.92 

681.88 

686.87 

691.89 

696.93 

702.02 

98 

707.U 

712.27 

717.44 

722.65 

727.89 

733-16 

738-46 

743.80 

749-  *  7 

754.57 

100 

760.00 

765-47 

770.97 

776.50 

782.07 

787.67 

*  This  table  is  based  on  Regnault's  experiments,  the  numbers  being  taken  from  Broch's  reduction  of  the  observa- 
tions (Trav.  et  Mem.  du  Bur.  Int.  des  Poids  et  Me"s.  torn.  i). 


SMITHSONIAN  TABLES. 


TABLE  137. 
PRESSURE    OF    AQUEOUS    VAPOR,    100°  C.    TO    230°  C. 

According  to  Regnault. 


153 


i 

0 

! 

Pressure  :  mm. 
of  mercury. 

Grammes  per  sq.  1 
centimetre. 

Pounds  per  sq. 
inch. 

Pressure  :  inches  1 
of  mercury. 

Pressure  : 
atmospheres. 

Temp.  °  Fahr. 

Temp.  °  Cent. 

*  i 

j| 

£ 

$ 

i! 

o 

Pounds  per  sq. 
inch. 

i! 

V    0 

1 

it 
£ 

Temp.  °  Fahr. 

100 

760.00 

1033.26 

14.70 

29.92 

1.000 

212.0 

150 

3581.2 

4868.9 

69.26 

I4I.O 

4.712 

302.0 

IOI 

787.59 

1070.78 

I5-23 

31.01 

.036 

213.8 

151 

3678.4 

5001.1 

71.14 

144.8 

.840 

303-8 

102 

816.01 

1109.41 

15-79 

32.13 

.074 

215.6 

152 

3777-7 

5I36-1 

73.06 

148.7 

.971 

305-6 

103 

845.28 

1149.21 

16.35 

33-28 

.112 

217.4 

153 

3879.2 

5275-0 

75-02 

152.7 

5.104 

3°74 

IO4 

875.41 

1190.17 

16.94 

34.46 

.152 

219.2 

3982.8 

5414.8 

77-03 

156.8 

.240 

309.2 

105 

106 

906.41 
938.3  ' 

1232.32 
1275.69 

Is." 

35.69 
36.94 

I-I93 

•235 

221.0 

222.8 

155 

156 

4088.6 
4196.6 

5558.6 
5705-5 

79.07 
81.22 

161.0 
165.2 

5-380 
.522 

3II.O 

312.8 

107 

971.14 

1320.32 

1878 

38.23 

.278 

224.6 

157 

4306.9 

5855-5 

83-29 

169.6 

.667 

3'4.6 

108 
109 

1004.91 
1039.65 

1366.24 
I4I347 

19.44 
20.  1  1 

39.56 
40.93 

.322 
368 

226.4 
228.2 

158 
159 

44I9.5 
45344 

6008.5 
6164.7 

85-47 
87.69 

174.0 
178.5 

.815 
.966 

316.4 
318.2 

110 

1075-37 

1462.03 

20.80 

42.34 

1415 

230.0 

160 

4651.6 

6324.2 

89.96 

183.1 

6.120 

320.0 

in 

112 

1112.09  '5"-97 
1149.83  1563.26 

21.51 

22.24 

43-78 

45.25 

463 

•5'3 

231.8 
233-6 

161 
162 

4771-3 
4893.4 

6486.8 
6652.8 

92.27 
94.63 

187.9 
192.7 

.278 

439 

321.8 
323-6 

"3 

1188.61 

1615.99 

22.99 

46.80 

•564 

2354 

163 

5OI7-9 

6822.2 

97.04  197.6 

.603 

3254 

114 

1228.47 

1670.18 

23.76 

48.37 

.616 

237.2 

164 

6994.9 

99-50 

202.6 

.770 

327.2 

115 

1269.41 

1725.84 

24-55 

49.98 

1.670 

239.0 

165 

5274.5 

7171.1 

IO2.OI 

2077 

6.940 

329.0 

116 
117 

1354.66 

1783.02 
1841.74 

25.37 
26.20 

5  '-63 
53-34 

.726 

.782 

240.8 
242.6 

1  66 
167 

5406.7 
5541-4 

7350-7 
7533-9 

104.56 
I07.I8 

212.9 
218.2 

7.114 
.291 

330.8 
332.6 

118 

1399.02 

1902.05 

27.06 

55-o8 

.841 

244.4 

1  68 

5678.8 

7720.7 

109.84 

223.6 

472 

3344 

119 

1444-55 

'963-95 

27.94 

56.87 

.901 

246.2 

169 

5818.9 

7911.1 

112.53 

229.1 

.656 

336.2 

120 

1491.28 

2027.48 

28.85 

58.71 

1.962 

248.0 

170 

5961.7 

8105.2 

115.29 

234.1 

7.844 

338.0 

121 

1539.25 

2092.70 

29.78 

60.61 

2.025 

249.8 

171 

6107.2 

8303-1 

n8.ii 

240.4 

8.036 

339-8 

122 

1  588.47 

2159.62 

3°-73 

62.54 

.091 

251.6 

172 

6255-5 

8504-7 

120.98 

246.3 

.231 

341.6 

I23 

1638.96 

2228.26 

31.70 

64-53 

•T57 

2534 

'73 

6406.6 

8710.2 

123.90 

252.2 

430 

343-4 

124 

1690.76 

2298.69 

32.70 

66.56 

.225 

255-2 

174 

6560.6 

8919.5 

126.87 

258.3 

.632 

345-2 

125 

1743.88 

2370.91 

33-72 

68.66 

2.295 

257.0 

175 

6717.4 

9132.8 

129.91 

264-5 

8.839 

347-0 

126 

J798-35 

2444.96 

34.78 

70.80 

258.8 

176 

6877.2 

9350-0 

133.00 

270.8 

9.049 

348.8 

127 

1854.20 

2520.89135.86 

73-oo 

•43° 

260.6 

177 

7040.0 

9571-3 

136-15 

277.2 

-263 

350.6 

128 

1911.47 

2598.76 

36.97 

75-25 

•5'5 

262.4 

178 

7205.7 

9796.6 

139-35 

2837 

.481 

3524 

129 

1970.15 

2678.54 

38.11 

77-57 

•592 

264.2 

179 

7374-5 

10026.1 

142.62 

290.3 

•703 

354-2 

130 

2030.28 

2760.29 

39.26 

79-93 

2.671 

266.0 

180 

7546.4 

10259.7 

1  45-93 

297.1 

9.929 

356.0 

131 

2091.94 

2844.12 

4047 

82.36 

•753 

267.8 

181 

7721.4 

10497.7 

149.32 

304.0 

10.150 

357-8 

132 
133 
134 

2155-03 
2219.69 
2285.92 

2929.89 
3017.80 

41.68 

42.93 
44-21 

84.84 

87-39 
89.99 

-836 
.921 
3.008 

269.6 
271.4 
273.2 

182 

183 

184 

7899-5 
8080.8 

8265.4 

10739.9 
10986.4 
11237.3 

152-77 
156.32 
159.84 

3II.O 
3l8.I 
3254 

i 

359-6 
361.4 
363-2 

135 

2353-73 

3200.04 

45-52 

92.67 

3-097 

275.0 

185 

8453-2 

11490.0 

16347 

332.3 

11.123 

365-0 

136 

2423.16 

329443 

46.87 

95-39 

.188 

276.8 

1  86 

8644.4 

II752-5 

167.17 

340.3 

-374 

366.8 

137 

2494-23 

3391.06 

48.24 

98.19 

.282 

278.6 

187 

8838.8 

12016.9 

170.94 

348.0 

.630 

368.6 

138 

2567.00 

3489.99 

49-65 

101.  06 

.378 

280.4 

188 

9036.7 

12285.9 

174.76 

355-8 

.885 

3704 

139 

2641.44 

359L29 

51.06 

103.99 

476 

282.2 

189 

9238.0 

12559.6 

178.65 

363-7 

12.155 

372.2 

140 

2717.63 

3694.78 

52-55 

106.99 

3-576 

284.0 

190 

9442.7 

12837.9 

182.61 

371-8 

12.425 

374-0 

141 
142 
143 

2795-57  3800.75154.07 
2875-3°  39°9-'  4  55-6o 
2956.86  4020.03  57.16 

1  1  0.06 
113.20 
116.41 

'783 
.890 

285.8 
287.6 
289.4 

191 

192 
193 

9650.9 
9862.7 
10078.0 

13121.0 
13408.9 
13701.7 

186.63 
190.72 
194.88 

380.0 
388.3 
396.8 

12.699 

12.977 
13.261 

375-8 
377-6 
379-4 

144 

3040.26 

4I33-42 

58.79 

119.69 

4.000 

291.2 

194 

10297.0 

13999-4 

199-13 

4054 

'3-549 

381.2 

145 

3125-55 

4249-37 

60.44 

123-05 

4-i  13 

293-0 

195 

10519.6 

14302.7 

203.43 

414.1 

13.842 

383-0 

146 

3212.74 

4367.91  62.13 

126.48 

.227 

294.8 

196 

10746.0 

14609.8 

207.81 

423.1 

I4.I39 

384-8 

147 
148 

33OI-87 
3392.98 

4489.09  ^63.86 
4612.96:65.62 

129.99 

-344 
464 

296.6 
298.4 

197 
198 

10975.0 
11209.8 

14921.2 
1  5240.4 

212.25 
216.77 

432.1 
441-3 

14.441 
14.749 

386.6 
3884 

149 

3486.09 

4739-55 

67.41 

137-25 

.587 

300.2 

199 

"447-5 

1  5  563-  5 

221.37 

450-7 

15.062 

390.2 

SMITHSONIAN  TABLES. 


154 


TABLES  1 37  (continued)^  39. 
PRESSURE  AND  WEIGHT  OF  AQUEOUS  VAPOR. 

TABLE  137  (continued).  —  Pressure  of  Aqueous  Vapor,  100°  0-230°  0. 
According  to  Regnault. 


1 

!t 

sf 

is 

Sf 
« 

I 
.§* 

j 

£ 

j 

i* 

Sf 

tj 

* 

If 

1 
•lb 

1 

I 

0 

d 

s| 

|] 

a, 

*"    O 

£*    V 
</3    £ 

Is 

0 

r' 

o 

d 

ii 

<o  o 

g.§ 

0, 

Ii 

g& 

3  § 

O 

d 

1 

b 

o" 

|-s 

r 

|S 

H 

1 

l§ 

I1 

<2  **•* 

&• 

5 

H 

200 

11689.0 

15891.9 

226.04 

460.1 

15,380 

392.0 

215 

15801.3 

21482.8 

305-57 

622.1 

20.791 

419.0 

2OI 
2O  2 
203 

1  1934.4 
12183.7 
12437.0 

16225.5  230.79 
16564.71235.61 

1  6908  .8  1240.  54 

469.8 

479-7 
489.6 

15-703 
16.031 
16.364 

393-8 
395-6 
397-4 

216 
217 
218 

16109.9 
16423.2 
16740.9 

21902.4 
22328.3 
22760.3 

317.62 

323-78 

634.2 
646.6 

6S9-I 

21.197 
21.690 
22.027 

420.8 
422.6 
424.4 

2O4 

12694.3 

17257.3 

245.49 

499-8 

16.703 

399-2 

219 

17063.3 

23198.6 

330.01 

671.8 

22.452 

426.2 

205 

12955-7 

17614.0 

250-53 

510.1 

17.047 

401.0 

220 

17390.4 

23643.2 

336.30 

684.7 

22.882 

428.0 

20b 

207 

13221.1 
13490.8 

17974.9 
18341.5 

255-67 
260.88 

520.5  17.396 
531.2117.751 

402.8 
404.6 

221 
222 

17722.1 
18058.6 

24094.3 
24551.8 

342.70 

349-21 

697.7 
711.0 

23-319 
23.761 

429.8 
431.6 

208 
209 

13764.5 
14042.5 

18713-7 
19091.6 

266.18 
27L55 

541-9 
552-9 

18.111 

18.477 

406.4 
408.2 

223 
224 

18746.1 

25015.8 
25486.4 

362.50 

724.4 
738.0 

24.210 
24.666 

433-4 
435-2 

210 

14324.8 

19475-4 

277.01 

S64-I 

18.848 

410.0 

225 

19097.0 

25963-5 

369.29 

75I-Q 

25.128 

437-0 

211 

14611.3 

19864.9 

282.58 

575-3 

19.226 

411.8 

226 

19452.9 

26447.4 

376.17 

765-8 

25-596 

438.8 

212 

14902.2 

20260.5 

288.21 

S86.7 

19.608 

413.6 

227 

19813.8 

26938.0 

383.1  s 

780.9 

26.07  1 

440.6 

213 

I5I97-5 

20661.9 

293.92 

598.3 

19.997 

4154 

228 

20179.6 

27435-4 

390.22 

794-5 

26-S52 

442.4 

214 

15497.2 

21069.3 

299.72 

610.2 

20.391 

417.2 

229 

20550.5  j  27939.6 

397-40 

809.0 

27.040 

444-2 

TABLE  138.  —  Weight  in  Grains  of  the  Aqueous  Vapor  contained  in  a  Cubic  Foot  of  Saturated  Air.* 


Temp. 

0.0 

1.0 

2.0 

3.0 

4.0 

6.0 

6.0 

7.0 

8.0 

9.0 

—10 

0.285 

0.270 

0.257 

0.243 

0.231 

0.218 

0.207 

0.196 

0.184 

0.174 

—  0 

0.481 

0-457 

0-434 

0.411 

0.389 

0-370 

0-350 

0.332 

0.316 

0.300 

+0 
10 

0.481 

0.776 

0.505 
0.816 

0.329 
0.856 

0-554 
0.898 

0.582 
0.941 

0.610 
0.985 

0.639 

1.032 

0.671 
1.079 

0.704 
1.128 

0-739 
1.181 

20 

1.235 

1.294 

1.355 

1.418 

1.483 

'•551 

1.623 

1.697 

'•773 

I-853 

30 

!-935 

2.022 

2.113 

2.194 

2.279 

2.366 

2-457 

2.550 

2.646 

2.746 

40 

2.849 

2-955 

3.064 

3-177 

3-294 

3-4M 

3-539 

3.667 

3.800 

3-936 

50 

60 

4.076 
5-745 

4.222 
5.941 

4-372 
6.142 

4-526 
6-349 

4.685 
6-563 

4.849 
6.782 

5.018 
7.009 

7.241 

5-370 
7.480 

5-555 
7.726 

70 

7.980 

8.240 

8.508 

8.782 

9.066 

9-356 

9.655 

9.962 

10.277 

1  0.60  1 

80 

10.934 

11.275 

11.626 

11.987 

12.356 

12.736 

13.127 

13.526 

13-937 

M-359 

90 

14.790 

15.234 

15.689 

16.155 

16.634 

17.124 

17.626 

18.142 

18.671 

19.212 

100 

19.766 

20-335 

20.917 

21.514 

22.125 

22.750 

23.392 

24.048 

24.720 

25.408 

no 

26.112 

26.832 

27.570 

28.325 

29.096 

29.887 

" 

*  See  "  Smithsonian  Meteorological  Tables,"  pp   132-133. 
TABLE  139.  —  Weight  in  Grammes  of  the  Aqueous  Vapor  contained  in  a  Cubic  Metre  of  Saturated  Air. 


Temp. 

0.0 

1.0 

2.0 

3.0 

4.0 

6.0 

6.0 

7.0 

8.0 

9.0 

—20 

—  10 

0.892 
2.154 

0.8  10 
1.978 

0-737 
1.811 

0.673 
1.658 

0.613 

0-557 
J-395 

0.505 
1.282 

0-457 
1.177 

0.413 
1.079 

0-373 
0.982 

—0 

4.835 

4468 

4.130 

3.813 

3-5!8 

3-244 

2.988 

2.752 

2.537 

2.340 

+0 

4.835 

5-T76 

5.538 

5-922 

6.330 

6.761 

7.219 

7-703 

8.215 

8-757 

10 

20 
30 

9-330 
17.118 
30.039 

9-935 
18.143 

3L704 

10.574 
19.222 

33-449 

11.249 

20-355 
35.275 

11.961 
21.546 
37-187 

12.712 
22.796 
39-187 

T3-505 
24.109 
41.279 

H-339 

25.487 

43-465 

15.218 
26.933 

45-751 

16.144 
28.450 
48/138 

SMITHSONIAN  TABLES. 


TABLE  140. 
PRESSURE   OF  AQUEOUS   VAPOR   IN   THE   ATMOSPHERE. 


155 


This  table  gives  the  vapor  pressure  corresponding  to  various  values  of  the  difference  t  —  ^  between  the  readings  of 
dry  and  wet  bulb  thermometers  and  the  temperature  ^  of  the  wet  bulb  thermometer.     The  differences  t  —  t^  are 

E:n  by  two-degree  steps  in  the  top  line,  and  t^  by  degrees  in  the  first  column.     Temperatures  in  Centigrade 
rees  and  Regnault's  vapor  pressures  in  millimetres  of  mercury  are  used  throughout  the  table.     The  table  was 
ulated  for  barometric  pressure  B  equal  to  76  centimetres,  and  a  correction  is  given  for  each  centimetre  at  the 
top  of  the  columns.* 


* 

t  —  f, 
=  0 

2 

4 

6 

8 

10 

12 

14 

16 

18 

20 

Difference  per 
i°of*-f, 

Corrections  for 
B  per  centi- 
metre, t 

.013 

.026 

.040 

•053 

.066 

.079 

.092 

.106 

.119 

.132 

—10 

I.96 

0.96 

O.IOO 

—9 

2.14 

1.14 

0.14 

O.IOO 

—8 

2-33 

J-33 

0-33 

O.IOO 

—7 

2-53 

!-53 

0-53 

Example. 

O.IOO 

—6 

2.76 

1.76 

0.76 

t  —  tl-=  7.2 

O.IOO 

5 

/!=  IO.O 

3.01 

2.01 

1.  00 

2?=:  74.5 

O.IOO 

—4 

3.28 

2.28 

1.27 

0.27 

Tabular  numbers  6.  12  —  6X.ioi=:   5.51 

O.IOO 

—3 

3-57 

2-57 

1.56 

0.56 

Correction  for  £=  1.5  X  .048  .  .  —     .07 

O.IOO 

—  2 

3.88 

2.88 

1.87 

0.87 

Hence  we  get/)  .  .  .  —  5.58 

O.IOO 

—  I 

4.22 

3-22 

2.21 

1.  21 

0.21 

O.IOO 

0 

4.60 

3.60 

2-59 

i-59 

0-59 

O.IOO 

I 

4-94 

3-93 

2.92 

1.92 

0.92 

O.IOO 

2 

5-3° 

4.29 

3-29 

2.28 

1.28 

0.27 

O.IOO 

3 

5.69 

4.68 

3-68 

2.67 

1.66 

0.66 

O.IOI 

4 

6.10 

5-09 

4.09 

3-o8 

2.07 

1.06 

0.05 

O.IOI 

5 

6-53 

5-52 

4.51 

3-50 

2.49 

1.48 

0.48 

O.IOI 

6 

7.00 

5-99 

4-98 

3-97 

2.96 

1.95 

0.94 

O.IOI 

7 

7-49 

6.48 

5-47 

4-45 

3-44 

2-43 

1.42 

0.41 

O.IOI 

8 

8.02 

7.01 

5.99 

4.98 

3-97 

2.96 

1.94 

0.93 

O.IOI 

9 

8-57 

7-56 

6-54 

5-53 

4-5i 

3-50 

2.49 

1.48 

0.46 

O.IOI 

10 

9.17 

8.16 

7.14 

6.12 

5-11 

4.09 

3-08 

2.07 

1.06 

0.05 

O.IOI 

ii 

9-79 

8.77 

7.76 

6.74 

5-73 

4.71 

3-69 

2.68 

1.66 

0.64 

O.IO2 

12 

10.46 

9-44 

8-43 

7.41 

6-39 

5-37 

4.36 

3-34 

2.32 

1.30 

0.28 

O.I  O2 

13 

ii.  16 

10.14 

9.12 

8.10 

7.09 

6.07 

5-°5 

4-03 

3-oi 

1.99 

0.97 

0.102 

14 

11.91 

10.89 

9.87 

8.85 

7-83 

6.8  1 

5-79 

4-77 

3-71 

2.69 

I.67 

O.I  O2 

15 

16 
17 

12.70 

13-54 
14.42 

11.68 
12.52 
13.40 

10.66 
11.50 

12.37 

9.64 
10.47 
"-35 

8.62 
9-45 
10.33 

7.60 
8-43 

6.58 

6.39 
7.26 

4-54 
5.37 
6.24 

3-52 
4-35 
5-22 

2-50 

3-33 
4.20 

O.I  O2 

0.102 
0.102 

18 

I5-36 

14-34 

13.31 

12.29 

11.26 

10.24 

9.2I 

8.19 

7.17 

6.15 

5-T3 

O.I  O2 

:9 

16.35 

I5-33 

14.30 

13.27 

12.25 

11.22 

IO.2O 

9.17 

8.15 

7.13 

6.1  1 

O.I  O2 

20 

17-39 

16.37 

J5-34 

I4-31 

13.28 

12.26 

11.23 

10.21 

9.18 

8.15 

7.12 

0.103 

21 

18.50 

1747 

16.45 

15.42 

H.39 

I3-36 

12-33 

11.31 

10.28 

9-25 

8.22 

0.103 

22 
23 

19.66 
20.89 

18.63 
19.86 

17.60 
18.83 

16.57 
17.80 

15-54 
16.77 

I4-51 
15.74 

13.48 
14.71 

12.46 
13.68 

n-43 
12.66 

10.40 
11.63 

I  O.6O 

0.103 
0.103 

24 

22.18 

21.15 

20.  1  2 

19.09 

18.05 

17.02 

14.96 

'3-94 

12.91 

11.88 

0.103 

25 

26 

23-55 
24.99 

22.52 
23.96 

21.49 

22.92 

20.45 
21.89 

19-43 
20.86 

18.39 
19.82 

I7-36 
18.79 

16.33 
17.76 

15.30 
16.73 

14.27 
15-70 

13.24 
14.67 

0.103 

0.103 

27 

26.51 

25.48 

2444 

23-40 

22.37 

21.34 

20.30 

19.27 

18.24 

17.21 

16.18 

0.103 

28 
29 

28.10 
29.78 

27.07 
28.75 

26.03 
27.71 

24.99 
26.67 

23-96 
25-63 

22.92 
24.59 

21.89 
23-56 

20.85 
22.52 

19.82 
21.49 

18.79 
20.46 

17.76 

0.103 
0.103 

30 

31-55 

30.51 

29.47 

28.43 

27.40 

26.36 

25-32 

24.29 

23-25 

22.22 

21.  18 

0.104 

31 

33-4i 

32.37 

31-33 

30.29 

29.25 

28.22 

27.18 

26.14 

25.10 

24.07 

23-03 

0.104 

32 

35-36 

34.32 

33-28 

32.24 

31.21 

30.17 

29.13 

28.09 

27.05 

26.01 

24.97 

0.104 

33 

3741 

36-37 

35-33 

34-29 

33-25 

32.22 

3I.l8 

30.14 

29.10 

28.06 

27.02 

0.104 

34 

39-57 

38.53 

37-48 

36-44 

35-40 

34.36 

33-32 

32.28 

31.24 

30.20 

29.16 

0.104 

35 

41.83 

40.79 

39-74 

38.70 

37-66 

36.62 

35-68 

34.64 

33-6o 

32.56 

3I-52 

0.104 

36 

44.20 
46.69 

43.16 
45-65 

42.11 
44.60 

41.07 
43-56 

40.03 
42.52 

38.99 
41.48 

37-95 
40-44 

36.90 

39-39 

35.86 
38.35 

34.82 
37-31 

33-78 
36.27 

0.104 
0.104 

38 

49-30 

48.26 

47-21 

46.17 

45-13 

44-08 

43-04 

41.99 

40.95 

39-91 

38-87 

0.104 

39 

52.04 

51.00 

49-95 

48.91 

47.86 

46.82 

45-77 

44-73 

43.78 

42.74 

41.69 

0.105 

*  The  table  was  calculated  from  the  formula  /=/t  —  0.00066  J3 (t  —  ^)  (1+0.00115^)  (Ferrel,  Annual  Report 
U.  S.  Chief  Signal  Officer,  1886,  App.  24). 

t  When  B  is  less  than  76  the  correction  is  to  be  added,  and  when  B  is  greater  than  76  it  is  to  be  subtracted. 

SMITHSONIAN  TABLES. 


I56 


TABLE  141. 


DEW- 


The  first  column  of  this  table  gives  the  temperatures  of  the  wet-bulb  thermometer,  and  the  top  line  the  difference 
the  table.  The  dew-points  were  computed  for  a  barometric  pressure  of  76  centimetres.  When  the  barometer  differs 
and  the  resulting  number  added  to  or  subtracted  from  the  tabular  number  according  as  the  barometer  is  below  or 


I 

,-*=i 

2 

3 

4 

6 

6 

7 

8 

Dew-points  corresponding  to  the  difference  of  temperature  given  in  the  above  line  and  the 
wet-bulb  thermometer  reading  given  in  first  column. 

87/5Z?  = 

.04 

.11 

.22 

•49 

—  10 

—  13.2 

—  17.9 

—  9 

12.0 

1  6.0 

—  22.0 

—  8 

10.7 

14-3 

194 

—  7 

9-5 

12.7 

I7.I 

—  24.0 

—  6 

8-3 

II.  2 

14.9 

20.3 

ST/SS  = 

•03 

.06 

.11 

.18 

•31 

•43 

—  5 

—  7-1 

—  9-7 

—  12-9 

—  17-5 

—  24-5 

—  4 

6.0 

8-3 

II.  I 

14.8 

20.  i 

—  3 

4.8 

6.9 

9-4 

12.6 

16.8 

—  234 

—  2 

3-6 

5-5 

7.8 

10.5 

13-9 

18.9 

—  I 

2-5 

4.2 

6.2 

8.5 

II-5 

154 

—  21.0 

57755  = 

.02 

.04 

.07 

.10 

.14 

.19 

.26 

•38 

0 

—  1.3 

—  2.9 

-4.8 

—  6.8 

—  12.3 

-I6.5 

—  22.9 

I 

o-3 

3-5 

5-3 

7.6 

10.2 

13-5 

18.3 

2 

+  0.6 

0.7 

2.2 

3-9 

6.1 

8-3 

II.  I 

14.7 

3 

1.7 

+  0.2 

1.0 

2.6 

4.6 

6.4 

8.9 

11.9 

4 

2.8 

1.4 

o.o 

1.3 

3-1 

4-7 

6.9 

94 

5778#  = 

.02 

•03 

•05 

.07 

.09 

.11 

.14 

.18 

5 

3-8 

2.6 

+  1.2 

—  O.I 

—  1.6 

—  3-2 

—  7.1 

6 

4-9 

3-7 

2-5 

+  1.1 

O.2 

3-3 

5-2 

7 

6.0 

4-9 

3-7 

2.4 

+  I.I 

o-3 

1.8 

34 

8 

7.0 

6.0 

4.9 

3-7 

2-5 

+  1.1 

o-3 

1.8 

9 

8.1 

7-1 

6.1 

5-° 

3-9 

2.6 

+  1.2 

O.I 

57755  = 

.01 

.02 

•03 

•05 

.06 

.08 

.10 

.12 

10 

9.1 

8.3 

7-3 

6-3 

5.2 

4.1 

2.8 

+  i-5 

ii 

IO.2 

9-3 

8.4 

7-5 

6-5 

5-5 

4-3 

12 

1  1.2 

10.4 

9.6 

8-7 

7-8 

6.8 

5-8 

4-7 

13 

12.3 

11.5 

10.7 

9.9 

9.1 

8.2 

7.2 

6.2 

14 

13-3 

12.6 

11.9 

n.  i 

10.3 

9-°5 

8.6 

7.6 

57/55  = 

.OI 

.02 

•03 

.04 

•05 

.06 

.07 

.08 

15 

14.4 

13-7 

13.0 

12.3 

10.8 

9-9 

9.1 

16 

15-4 

14.8 

14.1 

12.7 

I2.O 

11.3 

10.5 

17 
18 

16.4 

15.8 
16.9 

18.0 

17.4 

14.6 
16.9 

16.3 

13-3 

14-5 

12.6 

13.8 
iS-i 

1  1.8 
14.4 

57755  = 

•005 

.01 

.015 

.02 

.027 

•033 

.04 

•°5 

20 

21 

20.5 

19.0 

20.1 

19.6 

18.0 
19.1 

,     T74 
18.6 

16.9 

18.1 

16.3 

17-5 

15-7 
17.0 

22 

21.6 

21.  1 

20.7 

20.2 

19.7 

19.2 

18.7 

18.2 

23 

22.6 

22.2 

21.7 

21.3 

20.8 

20.4 

19.9 

194 

24 

23.6 

23.2 

22.8 

22.4 

22.O 

21.5 

21.  1 

20.6 

5  7755  = 

.005 

.01 

.015 

.02 

.025 

•03 

•035 

.04 

25 

24.6 

24-2 

23-9 

23-5 

23.1 

22.7 

22.2 

21.8 

26 

t6 

25-3 

24.9 

24-5 

24.2 

23.8 

234 

23.0 

27 

7 

26.3 

26.O 

25.6 

25-3 

24.9 

24-5 

24.1 

28 
29 
57/5,5  = 

.003 

27-3 
28.4 
.006 

27.0 
28.1 
.OI 

26.7 
27.8 
.013 

26.4 
27.4 
.017 

26.0 
27.1 
.019 

.022 

26.4 
.026 

30 

29.7 

29.4 

29.1 

28.8 

28.5 

28.2 

27.9 

27.6 

31 

30-7 

30-5 

30.2 

29.9 

29.6 

29-3 

29.0 

28.7 

32 

3i-7 

31-5 

31.2 

3°-9 

30-7 

304 

3O.I 

29.8  . 

33 

32.8 

32-5 

32.2 

32.0 

31-7 

3i-5 

31.2 

3°-9 

34 
57755  = 

33-8 
003 

33-5 
.005 

33-3 
008 

33-° 
.010 

32.8 
•013 

32-5 
.016 

32'3 
.019 

32.0 

.021 

35 

34-8 

34-5 

34-3 

34-i 

33-8 

33-6 

334 

33-  I 

36 

$ 

35-8 
36.8 
37-8 

Hi 

37-6 

35-3 
36-4 
37-4 

III 

37-2 

34-9 
36.0 

37-o 

34-6 

344 

34-2 
35-3 
364 

39 

38.8 

38.6 

38-4 

38.2 

38.0 

37-9 

37^ 

37-5 

SMITHSONIAN  TABLES. 


TABLE  141  (continued). 


157 


POINTS. 

between  the  dry  and  the  wet  bulb,  when  the  dew-point  has  the  values  given  at  corresponding  points  in  the  body  of 
from  76  centimetres  the  corresponding  numbers  in  the  lines  marked  ST/S3  are  to  be  multiplied  by  the  difference, 
or  above  76.  See  examples. 


«, 

«-<=. 

10 

11 

12 

13 

14 

15 

Dew-points  corresponding  to  the  difference  of  temperature  given  in  the  above  line  and  the 
wet-bulb  thermometer  reading  given  in  first  column. 

EXAMPLES. 

(i)  Given  .5—  72,  f^  =  10,  t  —  ^1  =  5. 

Then  tabular  number  for  ^  =  10  and  t  —  t^  —  5  is  5.2 
Also  76  —  72  =  4  and  S'J'/&£  =  .o6. 

Hence  the  dew-point  is                                •             5  44 

(2)  Given  2?  =  7i.s,  ^  =  7,*  —  ^  =  8. 

Then,  as  above,  tabulated  number^:         .        .    3.4 

- 

2 

Correction  =:o.  15  X  4.  5  =  67 

Dew-point  =      4.07 

5775.5  = 

•45 

.67 

0 

i 

2 

—  20.0 

3 

I5.8 

22.2 

4 

12-4 

1  6.8 

57/5^  = 

•23 

.29 

•37 

•44 

•54 

.66 

.72 

5 

—  19.8 

—  17.7 

6 

7-4 

IO.I 

134 

—  18.1 

7 

5-3 

7.6 

IO.I 

13-5 

-18.3 

8 

3-3 

5-2 

7-4 

IO.I 

13-5 

-18.3 

9 

3-2 

5-i 

7-2 

9.9 

I3>1 

—  17.2 

5  T/^B  = 

.14 

•17 

.20 

.22 

•25 

.29 

•36 

10 

o.o 

—  3-° 

—  4-7 

—  6.8 

—  94 

—  12.5 

ii 

+  1.8 

+  0.3 

I.O 

2.6 

4-3 

6-3 

8.8 

12 

3-5 

2.2 

+  0.8 

0.6 

2.1 

3-7 

5-7 

13 

5-1 

3-9 

2.7 

+  1.3 

O.I 

1.6 

3-1 

H 

6.7 

5.6 

4-5 

3-3 

+  I.9 

+  0-5 

0.9 

57/5^  = 

.09 

.11 

.12 

.14 

.16 

.18 

.20 

15 

-  16 

8.2 

9.6 

6 

6.2 

7.8 

& 

P 

2.7 
4-7 

3-5 

17 

II.O 

10.2 

9-4 

8.5 

7-5 

6-5 

5-5 

18 

12.4 

II.7 

10.9 

IO.I 

9.2 

8-3 

74 

19 

13.8 

I3>1 

12.4 

11.6 

10.8 

I  O.O 

9.1 

5775#  = 

.06 

.07 

.08 

.09 

.10 

.11 

•13 

20 

15.1 

14-5 

13-8 

12.4 

11.6 

108 

21 

16.4 

15.8 

15.2 

14-5 

13-9 

13.2 

12.5 

22 

17.6 

17.1 

16.5 

15-9 

15-3 

14.7 

14.0 

23 

18.9 

18.4 

17.9 

17-3 

1  6.8 

16.2 

15-7 

24 

20.  1 

19.6 

19.2 

18.7 

18.1 

17.6 

17.0 

5775.5  = 

•045 

.05 

.06 

.06 

.07 

.08 

.09 

25 

26 

21.4 

22.6 

20.9 

22.1 

20.4 
21.7 

'       20.0 
21.3 

20.8 

19.0 
20.3 

18.5 
19.9 

27 

23-7 

234 

22.9 

22.5 

22.1 

21.7 

21.2 

28 

24.9 

24-5 

24.2 

23.8 

234 

23.0 

22.6 

29 

26.1 

25-7 

25-4 

25.0 

24.6 

24.2 

23-9 

5775#  = 

.031 

•035 

.041 

.047 

•053 

.06 

.07 

30 

27.2 

26.9 

26.6 

26.2 

25-9 

25-5 

25.2 

31 

28.4 

28.1 

27.8 

27.4 

27.1 

26.8 

26.4 

32 

29-5 

29.2 

28.9 

28.6 

28.3 

28.0 

27.7 

33 

30.7 

30-4 

30.1 

29.8 

29-5 

29.2 

28.9 

34  • 

31.8 

31.5 

31.2 

3°-9 

30-7 

304 

3O.I 

5  775Z?  = 

.024 

.027 

.029 

.032 

•037 

•037 

.04 

35 

32.9 

32.6 

32-4 

32.1 

31.8 

31.6 

314 

36 

34-o 

33-7 

33-5 

33-3 

33-o 

32.8 

32-5 

P 

3^2 

34-9 
35-9 

34-6 

344 

34-2 

33-9 

35-i 

33-7 
34-8 

39 

37-3 

37-1 

36.8 

36.6 

364 

36.2 

36.0 

SMITHSONIAN  TABLES. 


'58 


TABLE  142. 
RELATIVE    HUMIDITY.1 


This  table  gives  the  humidity  of  the  air,  for  temperature  t  and  dew-point  d  in  Centigrade  degrees,  expressed 
in  percentages  of  the  saturation  value  for  the  temperature  t. 


Depression  of 
the  dew-point. 
t-d 

Dew-point  (d). 

Depression  of 
the  dew-point. 
t-d 

Dew-point  (d). 

10 

0 

+  10 

+  20 

+  30 

10 

0 

+  10 

+  20 

+  30 

C. 

C. 

o°.o 

100 

100 

100 

100 

100 

8°.0 

54 

57 

60 

62 

64 

0.2 

98 

99 

99 

99 

99 

8.2 

54 

56 

59 

61 

63 

0.4 

97 

97 

97 

98 

98 

8.4 

53 

56 

58 

60 

63 

0.6 

95 

96 

96 

96 

97 

8.6 

52 

55 

57 

60 

62 

0.8 

94 

94 

95 

95 

96 

8.8 

5i 

54 

57 

59 

61 

1.0 

92 

93 

94 

94 

94 

9.0 

51 

53 

56 

58 

61 

1.2 

9i 

92 

92 

93 

93 

9-2 

50 

53 

55 

58 

60 

1.4 

90 

90 

91 

92 

92 

94 

49 

52 

55 

57 

59 

1.6 

88 

89 

9° 

91 

91 

9.6 

48 

51 

54 

56 

59 

1.8 

87 

88 

89 

90 

90 

9.8 

48 

51 

53 

56 

58 

2.0 

86 

87 

88 

88 

89 

10.0 

47 

5° 

53 

55 

57 

2.2 

84 

85 

86 

87 

88 

10.5 

45 

48 

5i 

54 

2.4 
2.6 

83 
82 

84 
83 

85 
84 

86 

85 

87 
86 

II.O 

"•S 

44 
42 

47 
45 

49 
48 

52 
51 

2.8 

80 

82 

83 

84 

85 

12.0 

4i 

44 

47 

49 

3.0 

79 

81 

82 

83 

84 

12.0 

39 

42 

45 

48 

3-2 

78 

80 

81 

82 

83 

13.0 

38 

4i 

44 

46 

34 

77 

79 

80 

81 

82 

13-5 

37 

40 

43 

45 

3-6 

76 

77 

79 

80 

82 

14.0 

35 

38 

4i 

44 

3-8 

75 

76 

78 

79 

81 

14-5 

34 

37 

40 

43 

4.0 

73 

75 

77 

78 

80 

15.0 

33 

36 

39 

42 

4.2 

72 

74 

76 

77 

79 

"5-5 

32 

35 

38 

40 

4.4 

7i 

73 

75 

77 

78 

1  6.0 

3i 

34 

37 

39 

4.6 

70 

72 

74 

76 

77 

16.5 

3° 

33 

36 

38 

4-8 

69 

7i 

73 

75 

76 

17.0 

29 

32 

35 

37 

5.0 

68 

70 

72 

74 

75 

17.5 

28 

31 

34 

36 

5-2 

67 

7i 

73 

75 

18.0 

27 

30 

33 

35 

54 

66 

68 

70 

72 

74 

18.5 

26 

32 

34 

5.6 

65 

67 

69 

7i 

73 

19.0 

25 

28 

31 

33 

5.8 

64 

66 

69 

70 

72 

19-5 

24 

27 

30 

33 

6.0 

63 

66 

68 

70 

71 

20.0 

24 

26 

29 

32 

6.2 

62 

65 

67 

7i 

21.0 

22 

25 

27 

6.4 

61 

64 

66 

68 

70 

22.0 

21 

23 

26 

6.6 

60 

63 

65 

67 

23.0 

19 

22 

24 

6.8 

60 

62 

64 

66 

68 

24.0 

18 

21 

23 

7.0 

59 

61 

63 

66 

68 

25.0 

17 

IQ 

22 

7-2 

58 

60 

63 

65 

67 

26.0 

16 

18 

21 

74 

57 

60 

62 

64 

66 

27.0 

15 

17 

20 

7.6 

56 

59 

61 

63 

65 

28.0 

14 

16 

19 

7.8 

55 

58 

60 

63 

65 

29.0 

13 

15 

18 

8.0 

54 

57 

60 

62 

64 

30.0 

12 

H 

17 

*  Abridged  from  Table  45  of  "  Smithsonian  Meteorological  Tables," 
SMITHSONIAN  TABLES. 


TABLE  1 43. 
VALUES  OF  0.3786.* 

This  table  gives  the  humidity  term  0.378*,  which  occurs  in  the  equation 


h 

°76o:     -      7( 

for  the  calculation  of  the  density  of  the  dry  air  in  a  sample  containing  aqueous  vapor  at  pres- 
sure e;  do  is  the  density  at  normal  barometric  pressure,  B  the  observed  barometric  pressure, 
and  h  the  pressure  corrected  for  humidity.  For  values  of  -?-  see  Table  144.  Temperatures 
are  in  degrees  Centigrade,  and  pressures  in  millimetres  of  mercury. 


Dew 

Point. 

Vapor 
Pressure 
(ice). 

0.378*. 

Dew 
Point. 

Vapor 
Pressure 
(water). 

0.378*. 

Dew 

Point. 

e 
Vapor 
Pressure 
(water). 

0.378*. 

—5° 

0.034 

O.OI 

0 

4-579 

i-73 

+30 

31-555 

"•93 

45 

.061 

.02 

+  1 

4.921 

1.86 

31 

33-4I6 

12.63 

40 

.105 

.04 

2 

5.286 

2.OO 

32 

35-372 

13-37 

35 
30 

•173 
.292 

.07 
.11 

3 

4 

£y 

2.15 
2.30 

33 
34 

37427 
39-586 

14-15 
14.96 

—25 

0.484 

0.18 

5 

6.528 

2.47 

35 

4I-853 

15.82 

24 

•534 

.20 

6 

6.997 

2.65 

36 

44-23 

16.72 

23 

.589 

.22 

7 

7-494 

2.83 

37 

46.73 

17.66 

22 

.648 

.24 

8 

8.023 

3-03 

49-35 

18.65 

21 

.714 

.27 

9 

8.584 

3.24 

39 

52.09 

19.69 

—  20 

0.787 

0.30 

10 

9.179 

3-47 

40 

54.97 

20.78 

19 

.868 

•33 

ii 

9.810 

3-71 

41 

57.98 

21.92 

18 

-955 

•36 

12 

10-479 

3.96 

42 

61.13 

23.12 

11 

1.048 
1.148 

.40 
•44 

14 

11.187 
11.936 

4-23 
4.51 

43 
44 

64-43 
67.89 

38 

_  I5 

1-257 

0.48 

15 

12.728 

4.81 

45 

71.5° 

27.02 

H 

1-375 

•52 

16 

I3-565 

5-13 

46 

75.28 

28.46 

13 

1.506 

•57 

*7 

14.450 

5.46 

47 

79.23 

29-95 

12 
II 

1.650 
i.  806 

.62 
.68 

19 

'I'3?3 
16.367 

5.82 
6.19 

48 
49 

83-36 
87.67 

33-14 

—  10 

1.974 

0-75 

20 

17.406 

6.58 

5° 

92.17 

34-84 

9 

2.154 

.81 

21 

18.503 

6-99 

96.87 

36.62 

8 

2-347 

.89 

22 

19.661 

7-43 

52 

101.77 

38-47 

7 

2-557 

•97 

23 

20.883 

7.90 

53 

106.88 

40.40 

6 

2.785 

1.05 

24 

22.178 

8.38 

54 

112.21 

42.42 

—5 
4 

3-032 

\:ll 

25 
26 

23.546 
24.987 

8.90 
9-45 

II 

117.77 
123.56 

44-52 
46.71 

3 

2 

3-894 

1-47 

28 

26.505 
28.103 

IO.O2 
10.62 

P 

129.59 
135.87 

48.98 
51-36 

I 

4.223 

i.  60 

29 

29.785 

11.26 

59 

142.41 

53.83 

0 

4-579 

1-73 

30 

31-555 

"•93 

60 

149.21 

56.40 

*  This  table  is  quoted  from  "  Smithsonian  Meteorological  Tables,"  p.  225. 
SMITHSONIAN  TABLES. 


160  TABLES  144,  145. 

DENSITY  OF  AIR   FOR   DIFFERENT  PRESSURES  AND  HUMIDITIES. 


TABLE  144. -Values  of 


760' 


from  h  =  1  to  h  =  9,  for  the  Computation  of  Different  Values  of  the  Ratio 
of  Actual  to  Normal  Barometric  Pressure. 


This  gives  the  density  of  air  at  pressure  h  in  terms  of  the  density  at  normal  atmosphere  pressure.  When  the  air 
contains  moisture,  as  is  usually  the  case  with  the  atmosphere,  we  have  the  following  equation  for  the  dry  air 
pressure :  h  —  B — 0.378*?,  where  e  is  the  vapor  pressure,  and  B  the  observed  barometric  pressure  corrected  for 
temperature.  When  the  necessary  observations  are  made  the  value  of  e  may  be  taken  from  Table  170,  and  then 
0.378*  from  Table  172,  or  the  dew-point  may  be  found  and  the  value  of  0.378*  taken  from  Table  172. 


h 

h 
760 

1 

2 

3 

0.0x513158 
.0026316 
.0039474 

4 

0.0052632 
.0065789 
.0078947 

7 

8 
9 

0.0092105 
.0105263 
.0118421 

EXAMPLES  OF  USE  OF  THE  TABLE. 

To  find  the  value  of  —  when  h  =  754.3 
760 

h  —  700  gives  .92105 

50        l      .065789 

4        '      -005263 

•3  -000395 

754.3          .992497 


To  find  the  value  of  —  when  h  =  5.73 
760 

h  =  5  gives  .0065789 
.7  '  .0007895 
.03  "  .0000395 


5-73 


.0074079 


TABLE  145.  —Values  of  the  logarithms  of  ^  for  values  of  h  between  80  and  340. 

Values  from  8  to  80  may  be  got  by  subtracting  i  from  the  characteristic,  and  from  0.8  to  8  by  subtracting  2  from  the 

characteristic,  and  so  on. 


h 

Values  of  log  A. 
760 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

80 

7.O2228 

7.02767 

7.03300 

7.03826 

7.04347 

7.04861 

7.05368 

7.05871 

7.06367 

7.06858 

90 

•07343 

.07823 

.08297 

.08767 

.09231 

.09691 

.10146 

.10596 

.11041 

.11482 

100 

7.11919 

7.12351 

7.12779 

7.13202 

7.13622 

7.14038 

7.14449 

7.14857 

7.15261 

7.15661 

no 

.16058 

.16451 

.16840 

.17226 

.17609 

.17988 

.18364 

.18737 

.19107 

.19473 

1  20 

.19837 

.20197 

.20555 

.20909 

.21261 

.21611 

.21956 

.22299 

.22640 

.22978 

130 

•23313 

.23646 

.23976 

.24304 

.24629 

.24952 

•25273 

•25591 

.25907 

.26220 

140 

•26531 

.26841 

.27147 

.27452 

•27755 

•28055 

•28354 

.28650 

•28945 

.29237 

150 

7.29528 

7.29816 

7.30103 

7.30388 

7.30671 

7.30952 

7.31231 

7.31509 

7.31784 

7.32058 

1  60 

.32331 

.32601 

.32870 

•33137 

•33403 

.33667 

•33929 

.34190 

•3445° 

.34707 

170 

.34964 

.35218 

•35471 

•35723 

•35974 

.36222 

•36470 

.36716 

.36961 

•37204 

180 

•37446 

.37686 

.37926 

•38164 

.38400 

.38636 

.38870 

.39128 

•39334 

•39565 

190 

•39794 

.40022 

.40249 

.40474 

.40699 

.40922 

.41144 

•41365 

•41585 

.41804 

200 

7.42022 

7.42238 

7.42454 

7.42668 

7.42882 

7.43094 

7.43305 

7.43516 

7.43725 

7-43933 

210 

.44141 

•44347 

•44552 

•44757 

.44960 

.45162 

.45364 

•45565 

.45764 

•45963 

22O 

.46161 

•46358 

•46554 

•46749 

•46943 

.47137 

.47329 

•47521 

.47712 

.47902 

230 

.48091 

.48280 

.48467 

.48654 

.48840 

.49025 

.49210 

•49393 

.49576 

•49758 

240 

.49940 

.50120 

.50300 

.50479 

.50658 

.50835 

.51012 

.51188 

.51364 

•51539 

250 

7.51713 

7.51886 

7.52059 

7.52231 

7.52402 

7.52573 

7.52743 

7.52912 

7.53081 

7.53249 

260 

.53416 

•53583 

•53749 

•539*4 

•54079 

•54243 

.54407 

•5457° 

.54732 

.54894 

270 
280 

•55055 
•56634 

•552I6 
.56789 

•55376 
.56944 

•55535 
•57097 

•55694 
-57250 

•55852 
•57403 

.56010 

•57555 

.56167 
.57707 

•56323 

•57858 

•56479 
.58008 

290 

.58158 

.58308 

•58457 

.58605 

•58753 

.58901 

.59048 

.59194 

•59340 

.59486 

300 

7-59631 

7-59775 

7.59919 

7.60063 

7.60206 

7.60349 

7.60491 

7.60632 

7.60774 

7.60914 

310 

•61055 

.61195 

•6i334 

•6i473 

.61611 

.61750 

.61887 

.62025 

.62161 

.62298 

320 
33° 

.62434 
.63770 

.62569 
.63901 

.62704 
.64032 

.62839 
.64163 

.62973 
.64293 

.63107 
•64423 

.63240 
•64553 

.63373 
.64682 

.63506 
.64810 

.63638 
.64939 

340 

.65067 

.65194 

•65321 

.65448 

•65574 

.65701 

.65826 

.65952 

.66077 

.66201 

SMITHSONIAN  TABLES. 


TABLE  \  4$  (continued). 

DENSITY  OF  AIR. 


161 


Values  of  logarithms  of 


h 
760 


for  values  of  h  between  350  and  800. 


h 

Values  of  log  A. 
760 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

350 

T.66325 

1.66449 

1.66573 

1.66696 

1.66819 

1.66941 

1.67064 

1.67185 

7.67307 

1.67428 

360 

.67549 

.67669 

.67790 

.67909 

.68029 

.68148 

.68267 

.68385 

.68503 

.68621 

370 

.68739 

.68856 

•68973 

.69090 

.69206 

.69322 

.69437 

.69553 

.69668 

.69783 

380 

.69897 

.70011 

.70125 

.70239 

•70352 

•70463 

•70577 

.70690 

.70802 

.70914 

390 

.71025 

.71136 

.71247 

.71358 

.71468 

•71578 

.71688 

.71798 

.71907 

.72016 

400 

410 

T.72I25 
.73197 

1.72233 
•73303 

1.72341 
.73408 

1.72449 
•735H 

7.72557 
.73619 

1.72664 
.73723 

1.72771 
.73828 

1.72878 
•73932 

7.72985 
.74036 

1.73091 

.74140 

420 

.74244 

•74347 

•74450 

•74553 

.74655 

•74758 

.74860 

.74961 

.75063 

•75l64 

430 
440 

•75265 
.76264 

-7SA6 

.76362 

.76461 

.75567 
•76559 

.75668 
•76657 

•75768 
.76755 

.75867 
.76852 

.75967 
.76949 

.76066 
.77046 

.76165 
.77143 

450 

1.77240 

7.77336 

1.77432 

1.77528 

1.77624 

1.77720 

7.77815 

T.779IO 

1.78005 

1.78100 

460 

.78194 

.78289 

•78383 

•78477 

•78570 

.78664 

.78757 

.78850 

•79036 

470 
480 
490 

.79128 
^80938 

.79221 

.80133 
.81027 

.79313 
.80223 
.81115 

•79405 
•80313 
.81203 

.79496 
.80403 
.81291 

•79588 
•80493 
.81379 

.79679 
.80582 
.81467 

.79770 
.80672 
.81554 

.81642 

•79952 
.80850 
.81729 

500 

S10 
520 

T.8i8i6 
.82676 
•83519 

1.81902 
.82761 
.83602 

1.81989 
.82846 
.83686 

1.82075 
.82930 
.83769 

1.82162 
.83015 
.83852 

1.82248 
.83099 
•83935 

1.82334 
.83184 
.84017 

1.82419 
.83268 
.84100 

7.82505 

.83352 
.84182 

1.82590 

•83435 
.84264 

530 
540 

.84346 
•85158 

.84428 
.85238 

.84510 
•853I9 

.84591 
•85399 

•84673 
•85479 

.84754 
.85558 

.84835 
.85638 

.84916 
.85717 

.84997 
.85797 

.85076 
.85876 

550 

7.85955 

1.86034 

1.86113 

1.86191 

1.86270 

1.86348 

1.86426 

1.86504 

1.86582 

T.86660 

560 

•86737 

.86815 

.86892 

.86969 

.87047 

.87123 

.87200 

.87277 

•87353 

.87430 

570 

.87506 

.87282 

.87658 

•87734 

.87810 

.87885 

.87961 

.88036 

.88111 

.88186 

580 
590 

.88261 
.89004 

.88336 
.89077 

.88411 
.89151 

.88486 
.89224 

.88560 
.89297 

.88634 
.89370 

.88708 
.89443 

.88782 
.89516 

.88856 
.89589 

.88930 
.89661 

600 

1.89734 

1.89806 

1.89878 

1.89950 

1.90022 

1.90094 

1.90166 

1.90238 

7.90309 

1.90380 

610 
620 

.90452 
.91158 

•90523 
.91228 

.90594 
.91298 

.90665 
•91367 

.90735 
•9H37 

.90806 
.91507 

.90877 
.91576 

.90947 
.91645 

.91017 
•9I7I5 

.91088 
.91784 

630 

•91853 

.91922 

.91990 

.92059 

.92128 

.92196 

.92264 

.92333 

.92401 

.92469 

640 

•92537 

.92604 

.92672 

.92740 

.92807 

•92875 

.92942 

.93009 

.93076 

•93H3 

650 

1.93210 

1.93277 

1-93343 

1.93410 

1.93476 

T-93543 

1.93609 

7.93675 

7-93741 

7.93807 

660 

•93873 

•93939 

.94004 

.94070 

•94135 

.94201 

.94266 

•94331 

.94396 

.94461 

670 

.94526 

.94591 

.94656 

.94720 

•94785 

•94849 

•94913 

.94978 

.95042 

.95106 

680 

•95170 

•95233 

•95297 

.9536i 

.95424 

.95488 

•95551 

.95614 

•95677 

.95741 

690 

.95804 

.95866 

.95929 

.95992 

•96055 

.96117 

.96180 

.96242 

•96304 

.96366 

700 

1.96428 

1.96490 

1.96552 

1.96614 

1.96676 

7.96738 

1.96799 

1.96861 

1.96922 

7.96983 

710 

.97044 

.97106 

.97167 

.97228 

.97288 

•97349 

.97410 

•97471 

•97531 

•97592 

720 

.97652 

.97712 

.97772 

•97832 

.97892 

•9795  i 

.98012 

.98072 

.98132 

.98191 

73° 

.98251 

.98310 

.98370 

.98429 

.98488 

•98547 

•  .98606 

.98665 

.98724 

.98783 

740 

.98842 

.98900 

.98959 

.99018 

.99076 

•99U4 

•99*93 

.99251 

•99309 

.99367 

750 

1.99425 

1.99483 

1.99540 

1.99598 

1.99656 

1.99713 

1.99771 

1.99828. 

1.99886 

1.99942 

760 

o.ooooo 

0.00057 

0.00114 

0.00171 

0.00228 

0.00285 

0.00342 

0.00398 

0.00455 

0.00511 

770 

.00568 

.00624 

.00680 

.00737 

.00793 

.00849 

.00905 

.00961 

.01017 

.01072 

780 

.01128 

.01184 

.01239 

.01295 

•0135° 

.01406 

.01461 

.01516 

.01571 

.01626 

790 

.01681 

.01736 

.01791 

.01846 

.01901 

•01955 

.02010 

.02064 

.02119 

•02173 

SMITHSONIAN  TABLES. 


162  TABLE  146. 

VOLUME   OF   PERFECT  CASES. 


Values  of  1  +  . 00367 1. 

The  quantity  i  +  -00367 1  gives  for  a  perfect  gas  the  volume  at  t°  when  the  pressure 
is  kept  constant,  or  the  pressure  at  t°  when  the  volume  is  kept  constant,  in  terms 
of  the  volume  or  the  pressure  at  o°. 

(a)  This  part  of  the  table  gives  the  values  of  i  -f-  .00367 1  for  values  of  t  between  o° 
and  10°  C.  by  tenths  of  a  degree. 

(b)  This  part  gives  the  values  of  i  +  .00367 1  for  values  of  t  between  —  90°  and  +  1990° 
C.  by  10°  steps. 

These  two  parts  serve  to  give  any  intermediate  value  to  one  tenth  of  a  degree  by  a  sim- 
ple computation  as  follows  :  —  In  the  (b)  table  find  the  number  corresponding  to 
the  nearest  lower  temperature,  and  to  this  number  add  the  decimal  part  of  the 
number  in  the  (a)  table  which  corresponds  to  the  difference  between  the  nearest 
temperature  in  the  (&)  table  and  the  actual  temperature.  For  example,  let  the 
temperature  be  682°.2 : 

We  have  for  680  in  table  (6)  the  number  ....    3.49560 

And  for  2.2  in  table  (a)  the  decimal .00807 

Hence  the  number  for  682.2  is 3-50367 

(0)  This  part  gives  the  logarithms  of  i  +  .  00367  /for  values  of  t  between — 49°  and 

+  399°  C.  by  degrees. 

(d)  This  part  gives  the  logarithms  of  i  -f  .00367 1  for  values  of  t  between  400°  and  1990° 
C.  by  10°  steps. 

(a)  Values  of  1  +  . 00387*  lor  Values  of  *  between  0°  and  10°  0.  by  Tenths 
of  a  Degree. 


t 

0.0 

0.1 

0.2 

0.3 

0.4 

0 

1.  00000 

1.00037 

1.00073 

1.  001  10 

1.00147 

I 

.00367 

.00404 

.00440 

.00477 

.00514 

2 

.00734 

.00771 

.00807 

.00844 

.0088  I 

3 

.OIIOI 

.01138 

.01174 

.OI2II 

.01248 

4 

.01468 

•01505 

.01541 

.01578 

.01615 

5 

1.01835 

1.01872 

1.01908 

I.OI945 

1.01982 

6 

.02202 

.02239 

.02275 

.O23I2 

.02349 

7 

.02569 

.02606 

.02642 

.02679 

.02716 

8 

.02936 

.02973 

.03009 

.03046 

.03083 

9 

.03303 

•03340 

.03376 

•03413 

•03450 

t 

0.5 

0.6 

0.7 

0.8 

0.9 

0 

i 

1.00184 
.00550 

1.00220 
.00587 

1.00257 
.00624 

1.00294 
.00661 

1.00330 
.00697 

2 

.00918 

.00954 

.00991 

.01028 

.01064 

3 

.01284 

.01321 

.OI358 

•OI39S 

.01431 

4 

.01652 

.01688 

.01725 

.01762 

.01798 

5 

1.02018 

I.O2O55 

1.02092 

1.02129 

1.02165 

6 

.02386 

.02422 

.02459 

.02496 

•02332 

7 

.02752 

.02789 

.02826 

.02863 

.02899 

8 
9 

.03120 
.03486 

.03156 
•03523 

•03193 
.03560 

.03290 
•03597 

.03266 
•03633 

SMITHSONIAN  TABLES. 


TABLE  \  43  (continued).  163 

VOLUME   OF   PERFECT   CASES. 

Cb)  Values  of  1-f-. 00367  *  for  Values  of  t  between  —90°  and  +  1990°  0.  toy 
10°  Steps. 


t 

00 

10 

20 

30 

40 

—000 

1.  00000 

0.96330 

0.92660 

0.88990 

0.85320 

4000 

100 
2OO 
300 
400 

I.OOOOO 

1.36700 
1.73400 

2.IOIOO 

2.46800 

1.03670 
1.40370 
1.77070 
2.13770 
2.50470 

1.07340 
1.44040 
1.80740 
2.17440 
2.54140 

I.IIOIO 

1.47710 

1.84410 

2.21  1  10 
2.57810 

1.14680 
1.51380 
1.88080 
2.24780 
2.61480 

500 

600 
700 
800 
900 

2.83500 

3.20200 

3.56900 
3.93600 
4.30300 

2.87170 

3.23870 
3.60570 
3.97270 
4-33970 

2.90840 
3-27540 
3.64240 
4.00940 
4.37640 

2.94510 
3.3I2IO 
3.67910 
4.04610 
44I3IO 

2.98180 
3.34880 
3-7I580 
4.08280 
4.44980 

1000 

IIOO 
1200 
I3OO 
I4OO 

4.67000 

5.03700 
5.40400 
5.77100 
6.13800 

4.70670 
5-07370 
5.44070 
5.80770 
6.17470 

4-74340 
5.11040 
5-47740 
5.84440 
6.21140 

4.78010 
5.I47IO 

5-5I4Io 
5.88110 
6.24810 

4.81680 
5.18380 
5.55080 
5.91780 
6.28480 

1500 

1600 
1700 
1800 
1900 

6.50500 
6.87200 

7-23900 

7.60600 

7.97300 

6.54170 

6.90870 

7.27570 

7.64270 
8.00970 

6.57840 
6.94540 
7.31240 
7.67940 
8.04640 

6.61510 
6.98210 
7.34910 
7.71610 
8.08310 

6.65180 
7.01880 
7.38580 

& 

2000 

8.34000 

8.37670 

8.41340 

8.45010 

8.48680 

t 

50 

60 

70 

80 

90 

—000 

0.81650 

0.77980 

0.74310 

0.70640 

0.66970 

+000 

100 
200 

300 
400 

1.18350 

1-55050 
1.91750 

2.28450 
2.65150 

I.22O2O 
1.58720 
1.95420 
2.32120 
2.68820 

1.25690 
1.62390 
1.99090 
2.35790 
2.72490 

1.29360 
1.66060 
2.02760 
2.39460 
2.76160 

1.33030 
1.69730 
2.06430 
2.43130 
2.79830 

500 

600 
700 
800 
900 

3.01850 

3-38550 

3-75250 
4.11950 
4.48650 

3-05520 
342220 
3.78920 
4.15620 
4.52320 

3.09190 
3.45890 
3.82590 
4.19290 
4-55990 

3.12860 
3-49560 
3.86260 
4.22960 
4.59660 

3-I6530 

3-53230 
3-89930 
4.26630 

4.63330 

1000 

IIOO 

1  200 
1300 
1400 

4-85350 
5.22050 

5-58750 
5-95450 
6.32150 

4.89020 

5.25720 
5.62420 
5.99120 
6.35820 

4.92690 
5-29390 
5.66090 
6.02790 
6.39490 

4.96360 
5-33060 
5.69760 
6.06460 
6.43160 

5.00030 
5-36730 
5-7343° 
6.10130 
6.46830 

1500 

1600 
1700 
1800 
1900 

6.68850 

7-05550 
7.42250 
7.78950 
8.15650 

6.72520 
7.09220 
745920 
7.82620 
8.19320 

6.76190 
7.12890 
7-49590 
7.86290 
8.22990 

6.79860 
7.16560 
7.53260 
7.89960 
8.26660 

6.83530 
7.20230 
7-56930 
7-93630 
8.30330 

2000 

8.52350 

8.56020 

8.59690 

8.63360 

8.67030 

SMITHSONIAN  TABLES. 


i64 


TABLE  \^Q  (continued). 

VOLUME   OF 

(o)  Logarithms  of  1  +  .00367 1  for  Values 


t 

0 

1 

2 

3 

4 

Mean  diff. 
per  degree. 

—  40 

1.931051 

1.929179 

1.927299 

1.925410 

I-9235I3 

1884 

—  3° 

—  20 

.947546 
.965169 

•945744 
.963438 

.943934 
.961701 

.942117 
•959957 

1805 
1733 

—  10 

.983762 

.982104 

.980440 

•978769 

.977092 

1667 

—  0 

0.000000 

.998403 

.996801 

.995192 

•993577 

1605 

+  0 

0.000000 

0.001591 

0.003176 

0.004755 

0.006329 

1582 

IO 

•015653 

.017188 

.018717 

.020241 

.021760 

1526 

20 

30 
40 

.030762 

.045362 

.059488 

.032244 
.046796 
.060875 

.033721 
.048224 
.062259 

.035193 
.049648 
.063637 

.036661 
.051068 
.065012 

1474 
1426 
1381 

50 

60 

0.073168 

.086431 

0.074513 
•087735 

0.075853 
.089036 

0.077190 
.090332 

0.078522 
.091624 

1335 

1299 

B 

.099301 

.111800 

.100567 
.113030 

.101829 
.114257 

.103088 
.115481 

.104344 
.116701 

"59 
1226 

90 

.123950 

.125146 

.126339 

.127529 

.128716 

1191 

100 

0.135768 

0.136933 

0.138094 

0.139252 

0.140408 

H58 

no 

.147274 

.248408 

.149539 

.150667 

.151793 

1129 

120 

.158483 

.159588 

.160691 

.161790 

.162887 

IIOI 

130 

.169410 

.170488 

•171563 

.172635 

.173705 

1074 

140 

.180068 

.181120 

.182169 

.183216 

.184260 

1048 

150 

0.190472 

0.191498 

0.192523 

0.193545 

0.194564 

1023 

160 

.200632 

.201635 

.202635 

.203634 

.204630 

1000 

170 

•210559 

.211540 

.212518 

.213494 

.214468 

976 

i  So 

.220265 

.221224 

.222180 

.223135 

.224087 

956 

190 

.229759 

.230697 

.231633 

.232567 

.233499 

935 

200 

0.239049 

0.239967 

0.240884 

0.241798 

0.242710 

916 

210 
220 

.248145 
.257054 

.249044 
.257935 

.249942 
.258814 

.250837 
•259692 

.260567 

878 

230 

.265784 

.267510 

.268370 

.269228 

861 

240 

-274343 

.275189 

.276034 

.276877 

.277719 

844 

250 

0.282735 

0.283566 

0.284395 

0.285222 

0.286048 

828 

260 
270 

.290969 
.299049 

.291784 
.299849 

•292597 
.300648 

.293409 
.3OI445 

.294219 
.302240 

813 
798 

280 

.306982 

.307768 

•308552 

•309334 

.310115 

784 

290 

•314773 

.315544 

.3!63H 

.317083 

•3  17850 

769 

300 

0.322426 

0.323184 

0.323941 

0.324696 

0-325450 

756 

310 

.329947 

.330692 

•33M35 

•332178 

•3329I9 

743 

320 
33° 

•337339 
.344608 

.338072 
.345329 

.338803 
.345048 

•339533 
.346766 

.340262 
.347482 

730 
719 

340 

•351758 

•352466 

.353174 

.353880 

•354585 

707 

350 

360 

•365713 

0.359488 
.366399 

0.360184 
.367084 

0.360879 
.367768 

0.361573 

.368451 

§4 

370 

.372525 

.373201 

.373875 

•374549 

.375221 

674 

380 

.379233 

.380562 

.381225 

.381887 

664 

390 

•385439 

.$494 

.387148 

.387801 

.388453 

654 

SMITHSONIAN  TABLES. 


TABLE 
PERFECT   CASES. 

of  t  between  —49°  and  +399°  0.  by  Degrees. 


i6S 


t 

6 

6 

7 

8 

9 

Mean  diff. 
per  degree. 

—  40 

1.921608 

1.919695 

1.917773 

i"-9I5843 

1.913904 

1926 

—  30 

.940292 

.938460 

.936619 

•934771 

.932915 

1845 

—  20 

.958205 

.956447 

.954681 

•952909 

.951129 

1771 

—  10 

.975409 

•973719 

.972022 

.970319 

.968609 

1690 

—  0 

•99  i  957 

•990330 

.988697 

•987058 

.985413 

1636 

+  0 

0.007897 

0.009459 

0.011016 

0.012567 

0.014113 

1554 

10 

.023273 

.024781 

.026284 

.027782 

.029274 

1500 

20 

.038123 

.039581 

.041034 

.042481 

.043924 

1450 

3° 

.052482 

.053893 

.055298 

.056699 

.058096 

I4O2 

40 

.066382 

.067748 

.069109 

.070466 

.071819 

1359 

50 

0.079847 

0.081174 

0.082495 

0.083811 

0.085123 

1315 

60 

.092914 

.094198 

.095486 

•096765 

.098031 

I28l 

70 

•105595 

.106843 

.108088 

.109329 

.110566 

1243 

80 

.117917 

.119130 

.120340 

.121547 

.122750 

1210 

90 

.129899 

.131079 

.132256 

•133430 

.134601 

"75 

100 

0.141559 

0.142708 

0.143854 

0.144997 

0.146137 

1144 

no 

.152915 

.154034 

«I55I5I 

.156264 

•157375 

1115 

1  20 

.163981 

.164072 

.166161 

.167246 

.168330 

1087 

130 

.174772 

.175836 

.176898 

•177958 

.179014 

1060 

140 

.185301 

.186340 

.187377 

.188411 

.189443 

1035 

150 

0.195581 

0.196596 

0.197608 

0.198619 

0.199626 

ion 

160 

.205624 

.206615 

.207605 

.208592 

.209577 

988 

170 
180 

.215439 
.225038 

.216409 
.225986 

.217376 
.226932 

.218341 
.227876 

.219304 
.228819 

966 
946 

190 

.234429 

.235357 

.236283 

.237207 

.238129 

925 

200 

0.243621 

0.244529 

0.245436 

0.246341 

0.247244 

906 

210 
220 

.252623 
.261441 

>253512 
•262313 

.254400 
.263184 

•255287 
.264052 

.256172 
.264919 

887 
870 

230 

.270085 

.270940 

.271793 

.272644 

.273494 

853 

240 

•278559 

.279398 

.280234 

.281070 

.281903 

836 

250 

260 
270 

0.286872 
.295028 
.303034 

0.287694 
•295835 
.303827 

0.288515 
.296640 
.304618 

0.289326 
•297445 
.305407 

0.290153 
.298248 
.306196 

820 

805 
790 

280 
290 

.310895 
.318616 

.311673 
•3I938i 

.312450 
.320144 

.313226 
.320906 

.314000 
.321667 

776 
763 

300 

0.326203 

0.326954 

0.327704 

0.328453 

0.329201 

750 

310 
320 

.333659 
.340989 

.334397 
.341715 

.335135 
.342441 

•335871 
•343  i  64 

.336606 
.343887 

737 
724 

33° 

.348198 

.348912 

•349624 

.350337 

.351048 

713 

340 

.355289 

•355991 

•356693 

•357394 

.358093 

701 

350 

0.362266 

0.362957 

0.363648 

0.364337 

0.365025 

690 

360 

.369132 

.369813 

•370493 

.371171 

.371849 

678 

x-x-o 

370 

•375892 

.376562 

.377232 

.377900 

•378567 

668 

380 

.382548 

•383208 

.383868 

•384525 

•385183 

658 

390 

.389104 

.389754 

•390403 

.391052 

.391699 

648 

SMITHSONIAN  TABLES. 


1 66  TABLE  1 46  (continued). 

VOLUME   OF   PERFECT  CASES. 

(d)  Logarithms  of  1  +  . 00367*  lor  Values  ol  t  Detween  100°  and  1990°  0.  by  10°  Steps. 


1 

00 

10 

20 

30 

40 

400 

0.392345 

0.398756 

0.405073 

0.411300 

0.417439 

500 

600 
700 
800 
900 

0452553 
.505421 

•552547 
•595055 
•633771 

0.458139 

.510371 

•556990 
.599086 
.637460 

0.463654 
.515264 
.561388 
•603079 
.641117 

0.469100 
.520103 
.565742 
.607037 
.644744 

0.474479 
.524889 
.570052 
.610958 
.648341 

1000 

IIOO 

1  200 
1300 
1400 

0.669317 
.702172 

•732715 
.761251 
.788027 

0.672717 
•705325 
•735655 
.764004 

.790616 

0.676090 
•708455 
.738575 
.766740 
.793190 

0.679437 
•7  *  '563 
.74M75 
.769459 
795748 

0.682759 
.714648 
.744356 
.772160 
.798292 

1500 

1600 
1700 
1800 
1900 

0.813247 

.837083 

•839679 
.881156 

.901622 

0.81  5691 
.839396 
.861875 
.883247 
.903616 

0.818120 
.841697 
.864060 
.885327 
.905602 

0.820536 
•843986 
.866234 
.887398 
.907578 

0.822939 
.846263 
.868398 
.889459 
•909545 

t 

60 

60 

70 

80 

90 

400 

0.423492 

0.429462 

0-435351 

0.441161 

0.446894 

500 

600 

700 
800 
900 

0.479791 
•529623 
.574321 
.614845 
.651908 

0.485040 

•534305 
.57854§ 
.618696 
.655446 

0.490225 
•538938 
•582734 
.622515 
.658955 

0495350 

.543522 

.626299 
•662437 

o.  50041  c 
•548058 
.590987 
•630051 
.665890 

1000 

IIOO 

1  200 
1300 
1400 

0.686055 
.717712 
.747218 

•774845 
.800820 

0.689327 

•720755 
.750061 

777514 
•803334 

0.692574 
.723776 
.752886 
.780166 
.805834 

0.695797 
.726776 

•755692 
.782802 
.808319 

0.698996 
.729756 
•758480 
.785422 
.810790 

1500 

1600 
1700 
1800 
1900 

0.825329 
.848528 
.870550 
.891510 
.911504 

0.827705 
.850781 
.872692 
•893551 
•913454 

0.830069 

•853023 
.874824 

.895583 
•9I5395 

0.832420 
•855253 
•876945 
.897605 
.917327 

0.834758 

•857471 
.879056 
.899618 
.919251 

SMITHSONIAN  TABLES. 


TABLE  147. 


DETERMINATION  OF  HEIGHTS  BY  THE  BAROMETER, 


Formula  of  Babinet :  Z  =  C  BD °  ~  B . 
+  B 

•t  — 


C  (in  feet)  =  52494  |"i  +  /0  +  *  ~  64"|  English  measures. 
l_  900       J 

C  (in  metres)  =  16000  |~i  4-  2  (*o  +  O"!  metric  measures. 

L  1000        J 

In  which  Z  —  difference  of  height  of  two  stations  in  feet  or  metres. 
2?o>  B  =  barometric  readings  at  the  lower  and  upper  stations  respectively,  corrected  for  all 

sources  of  instrumental  error. 
/0,  t  =  air  temperatures  at  the  lower  and  upper  stations  respectively. 

Values  of  C. 


ENGLISH  MEASURES. 

METRIC  MEASURES. 

4(4  +  4 

C 

LogC 

I  Ob-Hi 

C 

LogC 

Fahr. 

Feet. 

Cent. 

Metres. 

10° 

49928 

4.69834 

—10° 

15360 

4.18639 

15 

505*  * 

•70339 

—8 

15488 

.19000 

—6 

15616 

•19357 

20 

25 

51094 
5l677 

4.70837 
•7133° 

—4 

—  2 

15744 
15872 

.19712 
.20063 

30 

52261 

4.71818 

0 

16000 

4.20412 

35 

52844 

.72300 

+  2 

16128 

.20758 

40 

53428 

472777 

6 

16256 

16384 

.2IIOI 
.21442 

45 

54011 

.73248 

8 

16512 

.21780 

50 

54595 

4.73715 

10 

16640 

4.22IIC 

55 

55178 

•74177 

12 

16768 

.22448 

H 

16896 

.22778 

60 

5576i 

474633 

16 

17024 

.23106 

65 

56344 

•75085 

18 

17152 

•23431 

70 

56927 

4-75532 

20 

17280 

4.23754 

75 

57511 

-75975 

22 

17408 

.24075 

80 

58094 

4.76413 

24 
26 

17536 
17664 

•24393 
.24709 

85 

58677 

•76847 

28 

17792 

.25022 

90 

59260 

4.77276 

30 

17920 

4.25334 

95 

59844 

.77702 

32 

18048 

•25643 

18176 

•25950 

100 

60427 

4.78123 

18304 

.26255 

SMITHSONIAN  TABLES. 


i68 


TABLE  148. 


BAROMETRIC 


Barometric  pressures  corresponding  to  different 
This  table  is  useful  when  a  boiling-point  apparatus  is  used 


(a)  Common  Measure.* 


Temp.  °  F. 

.0 

.1 

.2 

.3 

A 

.5 

.6 

.7 

.8 

.9 

185 

186 

17.06 
1742 

17.09 
17-47 

I7-I3 
I7-5I 

17.17 
17-54 

17.20 
17-58 

17.24 
17.62 

17.28 
17.66 

17.32 
17.70 

17.35 
17-74 

17-39 
17.77 

187 

188 

I7.8I 

18.20 

17.85 
18.24 

17.89 
18.28 

17-93 
18.32 

17.97 
18.36 

18.01 
18.40 

18.05 
18.44 

1  8.08 
18.48 

18.12 
18.52 

18.16 
18.56 

189 

190 

18.60 
19.00 

18.64 
19.04 

18.68 
19.08 

18.72 
19.12 

18.76 
19.16 

18.80 
19.21 

18.84 
19.25 

1  8.88 
19.29 

18.92 
19-33 

18.96 
19.37 

191 

192 

19.41 
19.83 

19-45 
19.87 

19.49 
19.91 

J9-54 
19.96 

19.58 

20.00 

19.62 
20.04 

19.66 
20.08 

19.70 
20.13 

!9-75 
20.17 

19.79 

20.21 

193 

194 

20.26 
20.68 

20.30 
20.73 

20.34 
20.78 

20.38 
20.82 

20.43 

20.86 

20.47 
20.91 

20.51 
20.95 

20.56 
20.99 

20.60 
21.04 

20.64 
2  1.  08 

195 

196 

21.13 
21.58 

21.17 
21.62 

21.22 
21.67 

21.26 
21.71 

21.31 
21.76 

21-35 
21.80 

21.40 
21.85 

21.44 
21.90 

21.48 
21.94 

2L53 
21.99 

197 

198 

22.03 
22.50 

22.08 

22.55 

22.13 

22.59 

22.17 
22.64 

22.22 
22.69 

22.27 
22.73 

22.31 
22.78 

22.36 
22.83 

22.41 

22.88 

22.45 
22.92 

199 

200 

22.97 
2345 

23.02 
23-50 

23.07 
23-55 

23.12 
23.60 

23.16 
23-65 

23.21 
23.70 

23.26 
23-75 

23.31 
23-79 

23-36 
23.84 

23.40 
23.89 

201 

202 

23-94 
24.44 

23-99 
24.49 

24.04 
24-54 

24.09 
24-59 

24.14 
24.64 

24.19 
24.69 

24.24 
24.74 

24.29 
24.79 

24-34 
24.85 

24.39 
24.90 

203 

204 

24-95 
25.46 

25.00 
25-52 

25-05 
25-57 

25.10 
25.62 

25.15 
25.67 

25.20 
25.72 

25.26 
25.78 

25-31 
25-83 

25-36 
25.88 

25.41 
25.94 

205 

206 

25-99 
26.52 

26.04 
26.58 

26.09 
26.63 

26.15 
26.68 

26.2O 
26.74 

26.25 
26.79 

26.31 
26.85 

26.36 
26.90 

26.41 

26.96 

26.47 
27.01 

207 

208 

27.06 
27.62 

27.12 
27.67 

27.17 

27-73 

27.23 
27.78 

27.28 
27.84 

2704 
27.90 

27.39 
27-95 

27-45 
28.01 

27.5! 
28.07 

27.56 
28.12 

209 

210 

28.18 
28.75 

28.24 
28.81 

28.29 
28.87 

28-35 
28.92 

28.41 
28.98 

28.46 
29.04 

28.52 
29.10 

28.58 
29.16 

28.63 

29.21 

28.69 
29.27 

211 

212 

29-33 
29.92 

29-39 
29.98 

29-45 
30.04 

29-51 
30.10 

29-57 
3O.l6 

29.63 
30.22 

29.68 
30.28 

29.74 
30.34 

29.80 
30.40 

29.86 
30.46 

SMITHSONIAN  TABLES. 


*  Pressures  in  inches  of  mercury. 


TABLE  1  48  (continued). 


PRESSURES. 


169 


temperatures  of  the  boiling-point  of  water. 

in  place  of  the  barometer  for  the  determination  of  heights. 


(b)  Metric  Measure.* 


Temp.  °  C. 

.0 

.1 

.2 

.3 

A 

.5 

.6 

.7 

.8 

.9 

80° 

354-9 

356.3 

357.8 

359-2 

360.7 

362.1 

363-6 

365.1 

366.5 

368.0 

81 

369.5 

371.0 

372.5 

374-0 

375-5 

377-0 

378.5 

380.0 

381.6 

383-1 

82 

384-6 

386.2 

3877 

389.3 

390-8 

392.4 

394-0 

395-5 

397.1 

398.7 

83 

400.3 

401.9 

403.5 

405.1 

406.7 

408.3 

409.9 

411.6 

413.2 

414.8 

84 

416.5 

418.1 

419-8 

421.4 

423.1 

424.8 

426.4 

428.1 

429.8 

43L5 

85 

433-2 

434-9 

436-6 

438.3 

440.0 

441-8 

443-5 

445-2 

447-0 

448.7 

86 

450.5 

452.2 

454.o 

455-8 

457-5 

459-3 

461.1 

462.9 

464-7 

466.5 

8? 

468.3 

470.1 

472.0 

473-8 

475-6 

477-5 

479-3 

481.2 

483.0 

484.9 

88 

486.8 

488.6 

490.5 

492.4 

494-3 

496.2 

498.1 

500.0 

501.9 

503-9 

89 

505.8 

507.7 

509-7 

511.6 

5I3-6 

515.6 

517.5 

5194 

521.5 

523-5 

90 

525.5 

527.5 

529.5 

531.5 

533-5 

535-5 

537-6 

539-6 

541.6 

543-7 

9i 

545-8 

547-8 

549-9 

552.0 

554-1 

556.2 

558.3 

560.4 

562.5 

564-6 

92 

566.7 

568.8 

571-0 

573-1 

575-3 

577-4 

579-6 

581.8 

584.0 

586.1 

93 

588.3 

590.5 

592-7 

595-0 

597-2 

5994 

601.6 

603.9 

606.1 

608.4 

94 

610.6 

612.9 

615.2 

6i7-5 

619.8 

622.1 

624.4 

626.7 

629.0 

631-3 

95 

633-7 

636.0 

638.4 

640.7 

643.1 

•  645-4 

647-8 

650.2 

652.6 

655-o 

96 

657-4 

659-8 

662.3 

664.7 

667.1 

669.5 

672.0 

674.5 

676.9 

679,4 

97 

681.9 

684.4 

686.9 

689.4 

691.9 

694.5 

696.9 

699.5 

702.0 

704.6 

98 

707.1 

709.7 

712.3 

714.9 

717.4 

720.0 

722.7 

725.3 

727.9 

730.5 

99 

733-2 

735-8 

738.5 

741.1 

743-8 

746.5 

749-2 

75J-9 

754-6 

757-3 

100 

760.0 

762.7 

765.5 

768.2 

771.0 

773-7 

776.5 

779-3 

782.1 

784.9 

SMITHSONIAN  TABLES. 


*  Pressures  in  millimetres  of  mercury. 


TABLES  149-151. 
STANDARD  WAVE-LENGTHS. 

TABLE  149.— Standard  Iron  Lines.    Fabry-Bulsson  Values. 

Referred  to  the  Cd  line,  ^=64  38.47  22. 

Source:  electric  arc;  current:  3-5  amperes;  voltage:  generally  no  volts. 


Wave-length. 

* 

Wave-length. 

* 

Wave-length. 

^ 

Wave-length. 

* 

2373737 
2413.310 

- 

3513.820 

—•145 
—.157 

4592.658 
4602.944 

—.182 

—.182 

5455-6l6 
5497-521 

—.218 
—.214 

2435.1598! 
2506.904  Si 

_ 

3606.681 
3640.391 

—.157 
—.144 

4647437 
4678.855 

—.180 
—.172 

5506.783 
5535-4I8 

—.217 
—.226 

2528.516 

- 

3677-628 

-.136 

4707.287 

—.170 

5569-632 

—.216 

2562.541 

— 

3724-379 

—.147 

4736.785 

-.178 

5586.770 

—  .221 

2588.016 
2628.296 

_ 

3753-6I5 
3805.346 

—.117 
—  .140 

4754.046  Mn 
4789.657 

—.179 
—.192 

5615.658 
5658-835 

—.219 
—.217 

2679.065 

- 

3843.261 

—.143 

4823.521  Mn 

-.176 

5709.396 

—.205 

2714.419 

— 

e6 

—.148 

4859.756 

—.172 

5760.843  Ni 

—.209 

2739-550 

— 

i 

—.147 

4878.226 

—.181 

5763.013 

—.205 

2778.225 

— 

_.  8 

—.147 

4903.324 

—.178 

5805.211  Ni 

—.230 

2813.290 

- 

3977-745 

-.146 

4919.006 

-.168 

5857.760  Ni 

—.216 

2851.800 

— 

4021.872 

—  .146 

4966.104 

—.166 

5892.882  Ni 

—.215 

2874.176 

- 

4076.641 

—  .151 

5001.880 

—  .164 

5934.683 

-.198 

2912.157 

- 

4118.552 

-.156 

5012.072 

—.180 

5952-739  , 

~  —  .204 

2941.347 

— 

4134.685 

—  -155 

5049.827 

—.181 

6003.039 

—  .2OO 

2987.293 

—  .146 

4147.677 

—•159 

5083-343 

—  -!75 

6027.059 

—  .215 

3030.152 

—.109 

4191.441 

—.154 

5110.415 

—.^59 

6065.493 

—  .2l6 

3075-725 
3125.661 

—•"5 
—.118 

4233-615 
4282.407 

=:$ 

5167.492 

-.169 
—.186 

6137.700 
6191.569 

—.215 
.210 

3I75-447 

—•"5 

4315.089 

—•173 

5192.362 

—.161 

6230.732 

—  .211 

3225.790 

—.129 

4352.741 

-.167 

5232-958 

-.164 

6265.147 

—  .2OI 

3271.003 

—.126 

4375-935 

—.172 

5266.568 

-.169 

6318.029 

—  .210 

3323-739 
3370.789 

—.142 
—.144 

4427.314 
4466.554 

—.168 
—-I73 

5302.316 
5324-196 

-.164 

—.177 

6335-343 
6393.612 

—  .211 
—.208 

3399-337 

—.152 

4494-572 

—.166 

537  i  -498 

-.236 

6430.859 

—.207 

3445-I55 

—.105 

453I-I55 

—.172 

5405.780 

—.209 

6494.994 

—.219 

3485.344 

—.149 

4547-854 

—.170 

5434-530 

.210 

Taken  from  Fabry  and  Buisson,  Astrophysical  Journal,  28,  1908. 

*  These  columns  give  the  differences:  Fabry-Buisson  minus  the  corresponding  iron  line  in  Rowland's  Preliminary 
Table  of  Solar  Spectrum  Wave-lengths. 

TABLE  150.  -Absolute  Wave-length  of  Red  Cadmium  Line  In  Air,  760  mm.    Pressure,  15°  0. 

6438.4722 Michelsen. 

6438.4696 Fabry  and  Perot. 

For  arc  and  spark  lines  of  titanium,  manganese,  and  vanadium  (on  above  system   of  wave-lengths),   see   Kilby, 

Astrophysical  Journal,  30,  1909. 


TABLE  161.  —  Some  ol  the  Stronger  Lines  of  Some  of  the  Elements. 


Barium    . 

5535-7 

Helium 

5875.8 

Magnesium 

5167.5 

Sodium     . 

5890.2 

Caesium  . 

4555-4 

" 

5876.2 

"     .    . 

5*72-9 

"      .    . 

5896.2 

Calcium  . 

4593-3 

Hydrogen 

4101.8 
4340-7 

Mercury  .   . 

5183.8 
5461.0 

Strontium 

M 

4607,5 
5481.2 

Cadmium 

4799.9 

"    . 

4861.5 

Potassium  . 

7668.5 

"       .      . 

6408.6 

"    .    . 

5085.8 

"    . 

6563.0 

M 

7701.9 

Thallium  . 

535°-6 

•   • 

6438.5 

Lithium 

6708.2 

Rubidium   . 

6298.7 

SMITHSONIAN  TABLES, 


TABLE  1 52. 
STANDARD   SOLAR   WAVE-LENGTHS.     ROWLAND'S   VALUES. 


171 


Wave-lengths  are  in  Angstrom  units  (10  Tmm.),  in  air  at  20°  C  and  76  cm.  of  mercury  pressure. 
The  intensities  run  from  I,  just  clearly  visible  on  the  map,  to  1000  for  the  H  and  K  lines;  below 
I  in  order  of  faintness  to  oooo  as  the  lines  are  more  and  more  difficult  to  see.  This  table  contains 
only  the  lines  above  5. 

N  indicates  a  line  not  clearly  defined,  probably  an  undissolved  multiple  line ;  s,  a  faded  appear- 
ing line ;  d,  a  double.  In  the  "  substance  "  column,  where  two  or  more  elements  are  given,  the 
line  is  compound  ;  the  order  in  which  they  are  given  indicates  the  portion  of  the  line  due  to  each 
element ;  when  the  solar  line  is  too  strong  to  be  due  wholly  to  the  element  given,  it  is  represented, 
-Fe,  for  example ;  when  commas  separate  the  elements  instead  of  a  dash,  the  metallic  lines  coin- 
cide with  the  same  part  of  the  solar  line,  Fe,  Cr,  for  example. 

Capital  letters  next  the  wave-length  numbers  are  the  ordinary  designations  of  the  lines.  A  indi- 
cates atmospheric  lines,  (wv),  due  to  water  vapor,  (O),  due  to  Oxygen. 


Wave- 
length. 

Substance. 

Inten- 
sity. 

Wave-length. 

Substance. 

Inten- 
sity. 

Wave- 
length. 

Sub- 
stance. 

Inten- 
sity. 

3037.5103 

Fe 

10  N 

3372.947 

Ti-Pd 

iod? 

3533-345 

Fe 

6 

3047.7253 

Fe 

20  N 

338o.722 

Ni 

6N 

3536-709 

Fe 

7 

3°53-53°S 

— 

7d? 

3414.911 

Ni 

15 

3541.237 

Fe 

7 

Mn,  Ni 

IO 

3423.848 

Ni 

7 

3542.232 

Fe 

6 

3057-552S 

Ti,  Fe 

20 

3433-7  i  5 

Ni,  Cr 

8d? 

3555-079 

Fe 

9 

3059.2123 
3067.3693 

Fe 
Fe 

20 

8 

34407623  )  Q 
3441.1553)  w 

Fe 
Fe 

20 
15 

3558.6723 
3565-535S 

Fe 

Fe 

12 

3073.091 

Ti,- 

6Nd? 

3442.ii8 

Mn 

6 

3566.522 

Ni 

10 

3078.7693 

Ti,  - 

8d? 

3444.0203 

Fe 

8N 

3570.2733 

Fe 

20 

3088.1455 

Ti 

7d? 

3446.406 

Ni 

15 

Ni 

6 

3134.2303 

Ni,  Fe 

8 

3449-583 

Co 

6d? 

3572.7i2 

Se,  - 

6 

3188.656 

-  Fe 

6d? 

3453-039 

Ni 

6d? 

3578.832 

Cr 

10 

3236.7033 

Ti 

7N 

3458.601 

Ni 

8 

358i.349s 

Fe 

3° 

3239.170 

Ti 

7 

3461.801 

Ni 

8 

3584.800 

Fe 

6 

3242.125 

Ti,- 

8 

3462.950 

Co 

6 

3585-I05 

Fe 

6 

3243-I89 

-,  Ni 

6 

3466.0153 

Fe 

6 

3585479 

Fe 

7 

3247.6883 

Cu 

10 

3475.5943 

Fe 

10 

Fe 

6 

3256.021 
3267.8343 
3271.129 

Fe? 
V 
Fe 

6 
6 
6 

3476.8493 
3483.923 
3485.493 

Fe 

Ni 
FeCo 

8 
6d? 
6 

3587-130 
3587.370 
3588.084 

Fe 
Co 

Ni 

8 

I 

3271.791 

Ti,  Fe 

6d? 

3490.733s 

Fe 

10  N 

3593-636 

Cr 

9 

3274.0963 

Cu 

IO 

3493-"4 

Ni 

10  N 

3594.784 

Fe 

6 

3277.482 

Co-Fe 

7d? 

3497.9823 

Fe 

8 

3597.854 

Ni 

8 

3286.898 
3295.9513 

Fe 
Fe,  Mn 

3500.9963 
3510.466 

Ni 
Ni 

6d? 
8 

3605.4793 
3606.8383. 

Cr 
Fe 

I 

3302.5103 

Na 

6 

3512.785 

Co 

6 

3609.0083 

Fe 

20 

3315.807 

Ni 

7d? 

Fe 

7 

3612.882 

Ni 

6d? 

3318.1603 

Ti 

6 

3515-206 

Ni 

12 

3617-9343 

Fe 

6 

3320.391 

Ni 

7 

3519.904 

N 

7 

3618.9193 

Fe 

20 

3336.820 

Mg 

8N 

3521.4103 

Fe 

8 

3619-539 

Ni 

8 

3349-597 

Ti 

7 

3524-677 

Ni 

20 

3621.6123 

Fe 

6 

3361-327 

Ti 

8 

3526.183 

Fe 

6 

3622.1473 

Fe 

6 

3365.908 

Ni 

6 

3526.988 

Co 

6 

3631.6053 

Fe 

15 

3366.311 

Ti,  Ni 

6d? 

3529.964 

Fe-Co 

6 

3640.5353 

Cr-Fc 

6 

3369-7I3 

Fe,  Ni 

6 

3533-I56 

Fe 

6 

3642.820 

Ti 

7 

Corrections  to  reduce  Rowland's  wave-lengths  to  Fabry  and  Buisson's  system  (the  accepted  standard,  1908).    Tem- 
perature 15°  C   pressure  760  mm. 

The  differences  "  (Fabry-Buisson-arc-iron) —  (Rowland-solar-iron) "  lines  were  plotted,  a  smooth  curve  drawn,  and 
the  following  values  obtained  : 

Wave-length        3000.        3100.        3200.        3300.        3400.         3500.        3600.        3700, 
Correction         — .106     — .115     — .124     — .137      — .148     — .154     — .155     — .140 


H.  A.  Rowland,  "A  preliminary  table  of  solar-spectrum  wave-lengths,' 
SMITHSONIAN  TABLES. 


Astrophysical  Journal,  1-6, 1895-1897. 


1/2  TABLE  1 52  (continue*), 

STANDARD  SOLAR  WAVE-LENGTHS.     ROWLAND'S    VALUES. 


Wave-length. 

Substance. 

Inten- 
sity. 

Wave-length. 

Substance. 

Inten- 
sity. 

Wave-length. 

Substance. 

Inten- 
sity. 

3647.9885 

Fe 

12 

3826.0273 

Fe 

20 

4045.9755 

Fe 

30 

3651'247 

Fe,- 

6 

3827.980 

Fe 

80 

4055.7015 

Mn 

6 

3651.614 

Fe 

7 

3829.5015 

Mg 

10 

4057.668 

- 

7 

3676.457 

Fe,  Cr 

6 

3831-837 

Ni 

6 

4063.7595 

Fe 

20 

3680.0695 

Fe 

9 

3832.4505 

Mg 

15 

4068.137 

Fe-Mn 

6 

3684.2585 

Fe 

7d? 

3834.364 

Fe 

IO 

4071.9085 

Fe 

15 

3685.339 

Ti 

icd? 

3838.4355 

Mg-C 

2C 

4077.8855 

Sr 

8 

3686.141 

Ti-Fe 

6 

3840.5805 

Fe-C 

8 

4i02.oooHS 

H,  In 

4oN 

3687.6105 

Fe 

6 

384I-I95 

Fe-Mn 

IO 

4121.4775 

Cr-Co 

6d? 

3689.614 

Fe 

6 

3845.606 

C-Co 

8d? 

4128.251 

Ce-V,- 

6d 

3701.234 

Fe 

8 

3850.118 

Fe-Cr 

10 

4i32-235 

Fe-Co 

IO 

3705.7085 

Fe 

9 

3856.5245 

Fe 

8 

Fe 

6 

3706.175 

Ca,  Mn 

6d? 

3857.805 

Cr-C 

6d? 

4140.089 

Fe 

6 

3709.3895 

Fe 

8 

3858.442 

Ni 

7 

4144.038 

Fe 

15 

3716.5915 

Fe 

7 

3860.0555 

Fe-C 

20 

4167.438 

_ 

8 

3720.0845 

Fe 

40 

3865-674 

Fe-C 

7 

4187.204 

Fe 

6 

3722.6925 

Ni 

10 

3872.639 

Fe 

6 

4i9I-595 

Fe 

6 

3724.526 

Fe 

6 

3878.152 

Fe-C 

8 

4202.1985 

Fe 

8 

3732.5453 

Co-Fe 

6 

3878.720 

Fe 

7Nd? 

4226-9O4sg 

Ca 

20  d? 

3733-469S 

Fe- 

7d? 

3886.4345 

Fe 

15 

4233.772 

Fe 

6 

3735.0145 

Fe 

40 

3887.196 

Fe 

7 

4236.112 

Fe 

8 

3737.2815 

Fe 

3° 

3894.211 

— 

8d 

4250.2875 

Fe 

8 

3738.466 

— 

6 

3895-803 

Fe 

7 

4250.9455 

Fe 

8 

3743-508 

Fe-Ti 

6 

3899.850 

Fe 

8 

4254-5053 

Cr 

8 

3745-7I7S 

Fe 

8 

3903.090 

Cr,  Fe,  Mo 

IO 

4260.6405 

Fe 

10 

3746.0585 

Fe 

6 

3904.023 

— 

8d 

4271.9345 

Fe 

15 

3748.4085 
3749.6315 

Fe 
Fe 

IO 

20 

3905.6605 
3906.628 

Si 
Fe 

12 
IO 

4274.9585 
4308.08  1  sG 

Cr 

Fe 

76? 

3753-732 

Fe-Ti 

6d? 

3920.410 

Fe 

10 

4325-939S 

Fe 

8 

3758.3753 
3759-447 
3760.196 

Fe 
Ti 
Fe 

I2d? 

5 

3923.054 
3928.0755 
3930.450 

Fe 
Fe 
Fe 

i2d? 
8 
8 

4376.1075 
4383.7205 

H 
Fe 
Fe 

20N 

6 
15 

3761.464 

Ti 

7 

3933.523 

- 

8N 

4404.9275 

Fe 

IO 

3763-9453 
3765.689 

Fe 
Fe 

10 

6 

3934.108      . 

Ca 
Co,  V-Cr 

IOOO 

8N 

4415.2935 
4442.510 

Fe 
Fe 

8 
6 

3767.3415 

Fe 

8 

3944.1605 

Al 

15 

4447.8925 

Fe 

6 

3775-7I7 

Ni 

7 

3956.819 

Fe 

6 

4494.7385 

Fe 

6 

3783.6745 

Ni 

6 

3957.1775 

Fe-Ca 

7d? 

4528.798 

Fe 

8 

3788.0465 

Fe 

9 

3961.6745 

Al 

20 

4534-139 

Ti-Co 

6 

3795.1475 
3798.6555 

Fe 
Fe 

6 

3968.350 

3968.62  5sH 

-,  Zr 
Ca 

6N 

700 

4549.808 
4554-21  is 

Ti-Co 
Ba 

6d? 
8 

3799-693s 

Fe 

7 

3968.886 

_ 

6N 

4572.1565 

Ti- 

6 

3805.4865 

Fe 

6 

3969.413 

Fe 

10 

4603.126 

Fe 

6 

3806.865 

Mn-Fe 

8d? 

3974.904 

Co-Fe 

6d? 

4629.5215 

Ti-Co 

6 

3807.293 

Ni 

6 

3977.8915 

Fe 

6 

4679.0275 

Fe 

6 

3807.681 

V-Fe 

6 

3986.9035 

- 

6 

4703.1775 

Mg 

10 

3814.698 

— 

8 

4005.408 

Fe 

7 

4714.5995 

Ni 

6 

3815.9875 

Fe 

15 

4030.9185 

Mn 

lod? 

4736-963 

Fe 

6 

3820.5865!, 

Fe-C 

25 

4033.2245 

Mn 

8d? 

4754.2255 

Mn 

7 

3824.591 

Fe 

6 

4034.6445 

Mn 

6d 

4783.6135 

Mn 

6 

Corrections  to  reduce  Rowland's  wave-lengths  to  Fabry  and  Buisson's  system  (the  accepted  standard,  1908).    Tem- 
perature 15°  C,  pressure  760  mm. 

Wave-length     3600.      3700.      3800.      3900.     4000.     4100.     4200.     4300.      4400.      4500.      4600.      4700.      4800. 
Correction      — .155  — .140  — .141  — .144  — .148  — .152  — .156  —.161  — .167  — .172  — .176  — .179  — .179. 

SMITHSONIAN  TABLES. 


TABLE  1  52  (continued).  172 

»  •J 

STANDARD   SOLAR   WAVE-LENGTHS.    ROWLAND'S   VALUES. 


Wave-length. 

Substance. 

Inten- 
sity. 

Wave-length. 

Substance. 

Inten- 
sity. 

Wave-length. 

Sub- 
stance. 

Inten- 
sity. 

486r.527sF 

H 

3° 

5948.7653 

Si 

6 

6563.o45sC 

H 

40 

4890.9483 

Fe 

6 

5985.0403 

Fe 

6 

6593.1613 

Fe 

6 

4891.683 

Fe 

8 

6003.2393 

Fe 

6 

6867.45736 

A(0) 

6d? 

4919.1743 

Fe 

6 

6008.7853 

Fe 

6 

6868.336} 

A(0) 

6 

4920.685 

Fe 

IO 

6013.7153 

Mn 

6 

6868.478  J1 

A(0) 

6 

4957-785S 

Fe 

8 

6016.8613 

Mn 

6 

6869.1423 

A(0) 

7 

5050.0083 
5i67-497sb4 

Fe 

Mg 

6 

15 

6022.0163 
6024.2813 

Mn 
Fe 

6 
7 

i£?SL 

A(0) 
A(0) 

6 

7  [d 

5171.7783 

Fe 

6 

6065.7093 

Fe 

7 

6870.249  ) 

A(0) 

5172.8  56sb2 

Mg 

20 

6102.3923 

Fe 

6 

6871.1803 

A(0) 

8 

5183.7913^ 

Mg 

30 

6102.9373 

Ca 

9 

6871.5328 

A(0) 

IO 

5233.1223 

Fe 

7 

6108.3343 

Ni 

6 

6872.4863 

A(0) 

ii 

5266.7383 

Fe 

6 

6122.4343 

Ca 

10 

6873.0803 

A(0) 

12 

5269-723sE 

Fe 

8d? 

6136.8293 

Fe 

8 

6874.0373 

A(0) 

12 

5283.8023 

Fe 

6 

61  37-9*5 

Fe 

7 

6874.8993 

A(0) 

13 

5324.3733 

Fe 

7 

6141.9383 

Fe,Ba 

7 

6875.8303 

A(0) 

13 

5328.236 
5340.121 

Fe 
Fe 

8d? 
6 

6i55-350 
6162.3903 

Ca 

7 
15 

6876.9583 
6877.8823 

A(0) 
A(0) 

13 
12 

5341-213 

Fe 

7 

6169.2493 

Ca 

6 

6879.2883 

A(0) 

12 

5367.6693 

Fe 

6 

6169.7783 

Ca 

7 

6880.1723 

A(0) 

6 

5370.1663 

Fe 

6 

6170.730 

Fe-Ni 

6 

6884.0763 

A(0) 

10 

5383-5783 

Fe 

6 

6i9T  -393s 

Ni 

6 

6886.0003 

A(0) 

II 

5397-344S 

Fe 

7d? 

6191.7793 

Fe 

9 

6886.9903 

A(0) 

12 

5405.9893 

Fe 

6 

6200.5273 

Fe 

6 

6889.1923 

A(0) 

13 

5424.2903 

Fe 

6 

6213.6443 

Fe 

6 

6890.1513 

A(0) 

14 

5429.911 

Fe 

6d? 

6219.4943 

Fe 

6 

6892.6183 

A(0) 

H 

5447.1303 
5528.6413 

Fe 

Mg 

6d? 
8 

6230.9433 
6246.5353 

V-Fe 
Fe 

8 
8 

6893.5603 
6896.2893 

A(0) 
A(0) 

15 

5569.848 

Fe 

6 

6252.7733 

-Fe 

7 

6897.2083 

A(0) 

15 

5573-075 

Fe 

6 

6256.5723 

Ni-Fe 

6 

6900.1993 

A(0) 

14 

5586.991 

Fe 

7 

6301.718 

Fe 

7 

6901.1173 

A(0) 

15 

5588.9853 

Ca 

6 

6318.239 

Fe 

6 

6904.3623 

A(0) 

14 

5615.8773 

Fe 

6 

6335-554 

Fe 

6 

6905.2713 

A(0) 

14 

5688.4363 

Na 

6 

6337.048 

Fe 

7 

6908.7833 

A(0) 

5711.3133 

Mg 

6 

6358.898 

Fe 

6 

6909.6763 

A(0) 

13 

5763.2183 

Fe 

6 

6393.8203 

Fe 

7 

6913.4483 

A(0) 

II 

5857.6743 

Ca 

8 

6400.2173 

Fe 

8 

6914-3375 

A(0) 

II 

5862.5823 

Fe 

6 

6411.8653 

Fe 

7 

6918.3703 

A(0) 

9 

5890.186302 

Na 

3° 

6421.5703 

Fe 

6919.2503 

A(0) 

9 

5896.155  DI 

Na 

20 

6439-  293S 

Ca 

8 

6923-553s 

A(0) 

9 

5901.6823 
5914.4303 

A(wv) 
-,  A(wv) 

6 
6 

6450.0333 
6494.0043 

Ca 
Ca 

6 
6 

6924.4273 

A(0) 
A,- 

69N 

5919.8603 
5930.4063 

A(wv) 
Fe 

5 

6495-2  i  3 
6546.4793 

Fe 

8 
6 

7206.692 

-  A 

6 

Corrections  to  reduce  Rowland's  wave-lengths  to  Fabry  and  Buisson's  system  (the  accepted  standard,  1908) ;  tem- 
perature 15°  C,  pressure  760  mm. : 

Wave-length        4800.        4900.        5000.        5100.        5200.        5300.        5400.        5500.        5600.        5700.        5800. 
Correction       — .179     — .176     — .173     — .170     — .166     — .17*     — .212     — .217     —.218     —.213     — .209 


Wave-length        5800.        5900.        6000.        6100.        6200.        6300.        6400.        6500.        6600. 
Correction        — .209     — .209     — .213     —.214     —.213      — .210     — .209    —.210. 

SMITHSONIAN  TABLES. 


6700.       6800. 


1/4  TABLE  153. 

STANDARD  WAVE-LENGTHS.    KAYSER'S  IRON  (ARC)  LINES. 

r=  easily  reversible. 


Wave- 
length. 

Inten- 
sity. 

Correc 

tion.* 

Wave- 
length. 

Inten- 
sity. 

Correc- 
tion.* 

Wave- 
length. 

Inten- 
sity. 

Correc- 
tion.* 

Wave- 
length. 

Inten- 
sity. 

Correc- 
tion.* 

2327.468 

3 

2518.198 

8r 

2742.506 

i  or 

2973.254 

8r 

31.38^: 

3 

22.950 

2or 

44.163 

8r 

7*366 

5r 

32.869 

3 

23-754 

4r 

44.624 

4r 

81.565 

7r 

38.073 

I 

i  or 

45-177 

5r 

83-690 

i  or 

43.567 

3 

29.22' 

8r 

46.580 

4r 

87.410 

4 

—.117 

48.196 

2 

33-9H 

4 

47-080 

5r 

90.511 

4 

48.380 

2 

35-699 

6r 

50.238 

i  or 

94-554 

i  or 

54.969 

2 

37-26; 

4r 

55.834 

5r 

2999.630 

8r 

59-I87 

3 

41.06^ 

8r 

56.412 

4r 

3001.068 

i  or 

60.079 

2 

44.016 

4r 

57413 

4r 

07.262 

2 

60.373 

2 

46.072 

I  or 

61.883 

5r 

07.409 

2r 

64.904 

2 

49.708 

8r 

62.125 

5r 

08.254 

8r 

66.678 

2 

56.404 

2 

68.621 

5r 

09.690 

4r 

68.670 

2 

56.963 

2 

72.205 

8r 

16.043 

3 

70.588 

2 

62.619 

5 

-.078 

78.327 

6r 

—  .102 

16.305 

3 

73-813 

3r 

—.076 

67.001 

4 

78.946 

2 

17-747 

8r 

75-273 
80.840 

3 
4 

75445 
78.012 

3 
3 

81.936 
88.207 

3 
lor 

20.619 
20.764 

i  or 

82.114 

84.623 

91.989 

3 

21.194 

i  or 

84.473 

3 

85.964 

3 

2797.877 

2 

25-960 

8r 

88.711 

2 

88.102 

—.086 

2804.622 

5r 

3L332 

4 

9I-563 

2 

98.456 

5r 

07.088 

5r 

31-753 

95.709 

5r 

9948j 

5r 

I3-39I 

8r 

—  .101 

37.505 

i  or 

2399.322 

5r 

2599.663 

4r 

17.612 

3 

41-753 

3 

2404.519 

3 

2606.920 

3r 

23.382 

5r 

41.860 

3 

04.969 

5r 

07.I55 

3r 

25.660 

6r 

47719 

i  or 

06.742 

5* 

11.963 

5r 

25-803 

4r 

5I-I79 

3 

10.601 

5r 

I3-9M 

4r 

32.543 

8r 

57-562 

8r 

11.152 

17.706 

4r 

35-562 

4r 

59.202 

I  or 

1  3-393 

4r 

—.083 

18.108 

2r 

38.231 

3r 

67-363 

8r 

24.231 
31.126 

3 

2 

23.627 

£ 

43-742 
44.083 

£ 

68.286 

75-850 

i 

—.125 

35-234 

(Si) 

—.075 

2^383 

5r 

-.087 

51.910 

5r 

—  .110 

8o.no 

2 

39-834 

4r 

3LJ39 

5r 

59.007 

3 

83-853 

5r 

40.201 

4r 

35-899 

3r 

63-973 

3 

91.687 

3 

42.658 

4r 

44.085 

3r 

67.679 

3 

95.013 

2 

47.808 

4r 

47.649 

3 

69.418 

3095-384 

2 

53.568 

2 

51.800 

2 

74.284 

5r 

—.108 

3100.057 

4r 

57-686 
62.279 

4r 

66^897 

3 
3' 

77-4H 
83.840 

3 
3 

00.418 
00.778 

4r 

62.740 

i  or 

73.3I5 

2 

90.000 

12.183 

2 

65.244 

5r 

79.148 

8r 

-.083 

94-617 

3 

16.747 

3 

68.974 

4r 

80.544 

3 

2899-531 

3 

25.770 

3 

—.109 

72.436 

4r 

89.302 

8r 

2901.496 

3 

32.627 

72.976 
74.906 

i  or 

4r 

90.153 
92.710 

2 

2 

07.630 
12.273 

i 

—.116 

40.503 
44.096 

3" 
3U 

78-657 

C 

2699.193 

3 

18.144 

3 

51.460 

79.872 
83.361 

i  or 
2or 

2706.672 
08.663 

2 

23.409 

25-479 

5 

57-157 
60.764 

4 
3 

83.618 

3r 

14.503 

5 

—.084 

29.119 

8r 

65.129 

3 

84.280 

8r 
i  or 

18.530 
19.121 

4*" 
lor 

37.030 
41.462 

i  or 

8r 

~.II5 

71473 
75.556 

3 
7 

—.109 

89^844 

8r 

20.997 

I  or 

44-5  T  9 

3 

78.122 

5 

90-737 

i  or 

23.671 

8r 

47.996 

So-339 

7 

91.249 

i  or 

25.024 

4r 

48.557 

4 

3 

93-331 

7r 

33.978 

8r 

54.061 

9r 

88.947 

5 

2496.625 

4r 

35.566 

8r 

57.484 

9r 

91.778 

2501.228 

8r 

37407 

i  or 

65-379 

7r 

92.921 

8 

07.991 

4r 

39-639 

8r 

—.089 

67.019 

i  or 

93-423 

8 

2510.927 

8r 

2742.349 

Sf 

2970.227 

i  or 

3199.638 

7 

Taken  from  Kayser's  Handbuch  der  Spectroscopie. 

*  For  reducing  to  Fabry  and  Buisson's  system  of  wave-lengths  see  Table  149  (the  accepted  standard,  1908);  tempera- 
ture 15°  C,  pressure  760  mm. 

SMITHSONIAN  TABLES. 


TABLE    1  53  (continued). 
STANDARD  WAVE-LENGTHS.    KAYSER'S  IRON  (ARC)  LINES. 

r  =  easily  reversible. 


175 


Wave- 
length. 

Inten- 
sity. 

Correc- 
tion.* 

Wave- 
length. 

Inten- 
sity. 

Correc- 
tion.* 

Wave- 
length. 

Inten- 
sity. 

Correc- 
tion.* 

Wave- 
length, 

Inten- 
sity. 

Correc- 
tion.* 

3200.595 

7 

3490.721 

6r 

3790.242 

5 

4107.646 

5 

°S-515 

8 

3497-989 

5r 

95«M9 

8r 

14.608 

4 

10.953 

5 

3506.650 

3 

3798.658 

6r 

18.709 

8 

—.157 

14.158 

10 

08.627 

2 

3801.822 

6r 

37.156 

6 

19.701 
19-935 

5 
5 

08.663 
13-974 

2 

—.154 

06.847 
13.202 

3U 

5 

54.662 

IOU 

4 

22.187 

i  or 

21.415 

5r 

15.987 

8r 

71.069 

4 

25.905 
31.091 

i  or 

8 

—•"5 

26.196 
26.822 

4 

20.573 
24.591 

g 

or 

75-799 
81.918 

5 

34-745 

8 

29.960 

3 

26.028 

8r 

87.221 

8 

8 

40.287 

2 

27.967 

7r 

91.611 

8 

—.170 

44.308 

5 

58.672 

cr 

34-370 

8r 

4199.256 

6 

48.333 

5 

65-535 

or 

40.586 

7r 

4202.195 

8 

51-357 

5 

70.257 

8r 

41.194 

8r 

10.521 

5 

57.724 

3 

81.348 

7r 

50.114 

8r 

J9-523 

5 

62.413 

2 

85478 

4r 

56.515 

6r 

22.387 

5 

65.746 

8 

87.137 

4r 

60.054 

lor 

27.606 

6 

71.129 
80.386 
84.720 

5 
5 
3 

—.126 

94.767 
3599781 
3605.619 

4u 

2 

4 

65.670 
72.640 
78.166 

6ru 
6r 

—.144 

33-771 
36.118 

45-423 

I 

5 

—  .146 

86.884 

7 

06.836 

4 

—.155 

78.722 

4 

47.604 

5 

3292.721 

5 

12.242 

2 

86.426 

6r 

50.299 

8 

3306.106 

7 

17-934 

5 

87.193 

5» 

50.948 

8 

06.479 

7 

18.918 

8r 

95.80I 

60.656 

9 

14.868 

5 

22.158 

5 

3899.853 

5r 

71-333 

7 

17.251 

2 

30.506 

3 

3903.097 

or 

71-933 

i  or 

28.992 

5 

31.617 

6r 

06.624 

6 

—.143 

82.567 

7 

—.160 

37-793 

4 

32.195 

5 

09.980 

3 

85.614 

4 

42.034 

3 

40.541 

5 

—.150 

I3-784 

91.631 

3 

48.056 

4 

47-997 

20.404 

6r 

94.290 

6r 

55-355 

4 

50-429 

3 

28.073 

5* 

4299.420 

6r 

66.917 

3 

51.615 

5 

41.032 

4 

4308.072 

7r 

67.675 

5 

3 

45.269 

2 

09.542 

4 

78.814 
80.242 

4 

59-673 
69.674 

5 
5 

48.927 
56.610 

4 
3 

'5-255 
25-94I 

6 

8 

—.166 

84.113 

4 

76.461 

3 

56.823 

5 

37.219 

6 

89.882 

2 

80.062 

66.219 

3 

46.739 

3 

94.721 

3 

83.205 

3 

69.411 

6r 

52.910 

5 

-.169 

3397-117 

3 

87.609 

77.892 

6 

—.147 

58.689 

3 

3402.392 

4 

3695.202 

3 

84.112 

4 

67.759 

5 

06.578 

2 

3702.180 

2 

86.330 

4 

69.954 

5 

06.938 

4 

05-7I4 

4r 

96.147 

3 

76.104 

6 

I3-275 

5 

09-395 

5r 

3998.211 

3 

83-724 

8r 

24.430 

5' 

20.083 

i  or 

4007.429 

3 

4391.  137 

4 

27.263 

4 

22.710 

6r 

I7.303 

2 

4404.929 

8 

40.762 

9r 

27.769 

5r 

22.029 

5 

—.157 

15-301 

8 

41.138 

8r 

33470 

30.670 

3 

27490 

6 

-.I76 

44-025 

7r 

35.016 

9r 

32.796 

2 

30.801 

5 

45-301 

5 

—.146 

37.278 

8r 

44.776 

2 

42.522 

6 

50.484 

4 

43-510 

6r 

45.978 

ior 

47.907 

6 

58.454 
60.067 

3 
4 

45-710 
48.409 

7r 

62.605 

3 

5 

54.572 
61.838 

4 
5 

66.006 

49.634 

8r 

63.755 

i  or 

66.737 

6 

—183 

7I-4I3 

3 

58-381 

8r 

68.138 

c 

69.566 

6 

71497 

3 

63.940 

8r 

71.901 

8r 

76.207 

6 

75.600 
76.850 

6r 
6r 

67.339 
76.606 

3 

79-999 
84.666 

3 

5 

84.420 
89.929 

5 
4 

83.159 
3485.490 

3 
3 

-.146 

78.670 
3788.031 

2 

5 

96.135 
4098.346 

5 
5 

4494-755 

6 

—.183 

Taken  from  Kayser's  Handbuch  der  Spectroscopie. 

*  For  reducing  to  Fabry  and  Buisson's  system  of  wave-lengths  see  Table  149  (the  accepted  standard,  1908) ;  tem» 
perature  is°C,  pressure  760  mm. 

SMITHSONIAN  TABLES. 


176  TABLE  154. 

WAVE-LENGTHS   OF   FRAUNHOFER   LINES. 

For  convenience  of  reference  the  values  of  the  wave-lengths  corresponding  to  the  Fraunhofer 
lines  usually  designated  by  the  letters  in  the  column  headed  "  index  letters,"  are  here  tabulated 
separately.  The  values  are  in  ten  millionths  of  a  millimetre,  on  the  supposition  that  the  D  line 
value  is  5896.155.  The  table  is  for  the  most  part  taken  from  Rowland's  table  of  standard  wave- 
lengths. 


Index  Letter. 

Line  due  to  — 

Wave-length  in 
centimetres  X  ic8. 

Index  Letter. 

Line  due  to  — 

Wave-length  in 
centimetres  X  ic8. 

(° 

7621.28* 

(Fe 

4308.081 

A 

/ 

G 

j 

(0 

7594.06* 

<Ca 

4307.907 

a 

.  - 

7164.725 

g 

Ca 

4226.904 

B 

0 

6870.182! 

horH5 

H 

4I02.00O 

'    C  or  Ha 

H 

6563-045 

H 

Ca 

3968.625 

a 

0 

6278.303  J 

K 

Ca 

3933.825 

•         * 

Na 

5896.155 

L 

Fe 

3820.586 

V        D2 

Na 

5890.186 

M 

Fe 

3727.778 

DS 

He 

5875-985 

N 

Fe 

358L349 

Ei 

f  Fe 

5270.558 

O 

Fe 

3441.155 

(Ca 

5270.438 

P 

Fe 

336L327 

E2 

Fe 

5269.723 

Q 

Fe 

3286.898 

bi 

Mg 

5I8379I 

(Ca 

3181.387 

R 

< 

b2 

Mg 

5172.856 

(Ca 

31  79-453 

(Ft 

5169.220 

Fe 

3100.787 

b8 

] 

Si) 

(•Fe 

5169.069 

-  Fe 

3100.430 

S2) 

(Fe 

5167.678 

Fe 

3100.046 

b* 

1 

(Mg 

5l67497 

s 

Fe 

3047.725 

*     F  or  Hp 

H 

4861.527 

T 

Fe 

3020.76 

d 

Fe 

4383-721 

t 

Fe 

2994-53 

G'  or  Hy 

H 

4340-634 

U 

Fe 

2947.99 

f 

Fe 

4325.939 

*  The  two  lines  here  given  for  A  are  stated  by  Rowland  to  be :  the  first,  a  line  "  beginning  at  the  head  of  A,  out- 
side edge  ;  "  the  second,  a  "  single  line  beginning  at  the  tail  of  A." 
t  The  principal  line  in  the  head  of  B. 


Chief  line  in  the  a  group. 

See  Table  152,  Rowland's  Solar  Wave-lengths  (foot  of  page)  for  correction  to  reduce  these  values  to  Fabry-Buisson 
system  of  wave-lengths. 

SMITHSONIAN  TABLES. 


TABLE  1 55.  177 

PHOTOMETRIC  STANDARDS 

No  primary  photometric  standard  has  been  generally  adopted  by  the  various  governments.  In 
Germany  the  Hefner  lamp  is  most  used ;  in  England  the  Pentane  lamp  and  sperm  candles  are 
used ;  in  France  the  Carcel  lamp  is  preferred;  in  America  the  Pentane  and  Hefner  lamps  are  used 
to  some  extent,  but  candles  are  more  largely  employed  in  gas  photometry.  For  the  photometry 
of  electric  lamps,  and  generally  in  accurate  photometric  work,  electric  lamps,  standardized  at  a 
national  standardizing  institution,  are  commonly  employed. 

The  "  International  candle  "  is  the  name  recently  employed  to  designate  the  value  of  the  candle 
as  maintained  by  cooperative  effort  between  the  national  laboratories  of  England,  France,  and 
America;  and  the  value  of  various  photometric  units  in  terms  of  this  international  candle  is  given 
in  the  following  table  (taken  from  Circular  No.  1 5  of  the  Bureau  of  Standards). 

I  International  Candle  =  i  Pentane  Candle, 
i  International  Candle  =  I  Bougie  Decimale. 
I  International  Candle  =  i  American  Candle, 
i  International  Candle  =  1.11  Hefner  Unit, 
i  International  Candle  =  0.104  Carcel  Unit. 

Therefore  i  Hefner  Unit  =  0.90  International  Candle. 

The  values  of  the  flame  standards  most  commonly  used  are  as  follows : 

1.  Standard  Pentane  Lamp,  burning  pentane 10.0  candles. 

2.  Standard  Hefner  Lamp,  burning  amyl  acetate 0.9  candles. 

3.  Standard  Carcel  Lamp,  burning  colza  oil 9.6  candles. 

4.  Standard  English  Sperm  Candle,  approximately    ....  i.o  candles. 

Slight  differences  in  candle  power  are  found  in  different  lamps,  even  when  made  as  accurately 
as  possible  to  the  same  specifications.  Hence  these  so-called  primary  standards  should  be  them- 
selves standardized. 

SMITHSONIAN  TABLES. 


178  TABLES  156-158. 

SENSITIVENESS  OF  THE  EYE  TO  RADIATION. 

(Compiled  from  Nutting,  Bulletin  of  the  Bureau  of  Standards.) 

Radiation  is  easily  visible  to  most  eyes  from  0.330/1  in  the  violet  to  0.770;*  in  the  red.  At  low 
intensities  approaching  threshold  values  (red  vision)  the  maximum  of  spectral  sensibility  lies 
in  the  green  at  about  0.510/1  for  90%  of  all  persons.  At  higher  intensities  with  the  establish- 
ment of  cone  vision  the  maximum  shifts  towards  the  yellow  at  least  as  far  as  0.560,0. 


TABLE  156. 


Variation  of  the  Sensitiveness  of  the  Eye  with  the  Wave-length  at  Low  Intensities  (near 
Threshold  Values).    Konig. 


\ 

.410 

.430 

•450 

.470 

.490 

.510 

•530 

•550 

•570 

.590 

.610 

Mean  sensitiveness 

O.02 

0.06 

0.23 

0.49 

0.8  1 

1.  00 

o.Si 

0.49 

0.22 

0.077 

0.026 

TABLE  157.  —  Variation  of  Sensitiveness  to  Radiation  of  Greater  Intensities. 

The  sensibility  is  approximately  proportional  to  the  intensity  over  a  wide  range.  The  ratio  of 
optical-  to  radiation-intensity  increases  more  rapidly  for  the  red  than  for  the  blue  or  green 
(Purkinje  phenomenon). 

The  intensity  is  given  for  the  spectrum  at  0.535/4  (green). 


Intensity  (metre-candles)  = 
Ratio  to  preceding  step  = 

.00024 

.00225 

9.38 

.0360 
16 

•575 
16 

2.30 

9.22 

36.9 

147.6 

590.4 

Wave-length,  A. 

Se 

isitivenes 

s. 

0.430/4 

.081 

.093 

.I27 

.128 

.114 

.114 

_ 

- 

- 

•450 

•33 

•30 

.29 

•31 

•23 

•175 

.16 

- 

- 

.470 

•63 

•59 

•54 

•y 

.51 

.29 

.26 

•23 

— 

.490 

•5°5 

I.OO 

I.OO 

(-76) 

I.OO 

(.89) 

I.OO 

(•*3) 
•99 

•5° 

(.76) 

Jg 

61 

•35 
•54 

.520 
•535 

.88 
.61 

.86 
.62 

.86 
.63 

•94 

.72 

•99 
.91 

(.85) 
(.98) 

.85 
.98 

.85 
•99 

.82 
.98 

•555 

.26 

•3° 

•34 

.41 

.62 

.84 

•93 

•97 

•575 

.074 

.102 

.122 

.168 

(-39) 

(.63) 

(.76) 

(.82) 

(.84) 

•590 

.025 

•034 

•054 

.091 

.27 

•49 

.61 

.68 

.69 

.605 

.008 

.012 

.024 

.056 

•173 

•35 

US) 

•54 

•55 

.625 

.004 

.004 

.Oil 

.027 

.098 

.20 

•27 

•35 

•35 

,650 

.000 

.000 

.003 

.007 

.025 

.060 

.085 

.122 

•133 

.670 

.000 

.000 

.001 

.002 

.007 

.017 

.025 

.030 

.030 

A,  maximum  sensitiveness 

•503 

•504 

•5°4 

.508 

•513 

•530 

.541 

•543 

•544 

TABLE  158.  —  Sensibility  to  Small  Differences  in  Intensity  measured  as  a  Fraction  of  the  Whole. 


A  — 

.670 

.605 

•575 

•505 

.470 

•430 

White 

I0inm.  c.  = 

0.060 

0.0056 

0.0029 

O.OOOIJ 

O.OOOI2 

0.00012 

0.00072 

j 

81: 

'.  Konig's  data,  measures  from  one  r 

ormal 

person  < 

inly. 

1,000,000 

_ 

- 

- 

- 

- 

- 

.036 

200,000 

— 

.042 

— 

— 

— 

— 

.027 

100,000 

— 

.024 

.032 

— 

-» 

•• 

.019 

50,000 

.021 

•025 

.026 

- 

- 

- 

.017 

20,000 

.Ol6 

.018 

.020 

.019 

— 

— 

.017 

10,000 

.Ol6 

.016 

.Ol8 

.018 

_ 

• 

.018 

5,000 

.Ol8 

.016 

.017 

.016 

_ 

_ 

.018 

2,000 

.Ol6 

.018 

•  Ol8 

.017 

.018 

- 

.018 

1,000 

.017 

.020 

.018 

.018 

.017 

.018 

.018 

500 

.020 

•  O2  1 

•  018 

.019 

.018 

.021 

.019 

200 

.022 

•022 

.022 

.022 

.021 

.024 

.023 

100 

.02Q 

.028 

.027 

.024 

.022 

.025 

.030 

5° 

.038 

.038 

•032 

.025 

.025 

.027 

.032 

10 

.065 

.o6l 

•058 

.036 

•037 

.040 

.048 

5 

.092 

.103 

.089 

.049 

.046 

.049 

.059 

I 

.258 

.212 

.170 

.080 

.088 

.074 

•  I23 

0.5 

.376 

.276 

.21 

.091 

.096 

.097 

.188 

O.IO 

.40 

.133 

.138 

•137 

•377 

0.05 

- 

- 

.183 

.I8S 

•154 

.484 

O.OI 

— 

— 

— 

.271 

.289 

.249 

— 

0.005 

" 

•325 

•  300 

.312 

The  sensibility  to  small  differences  in  inten- 
sity is  independent  of  the  intensity  (Fech- 
ner's  law).  About  0.016  for  moderate 
intensities.  Greater  for  extreme  values. 

It  is  independent  of  wave-length,  extremes 
excepted  (Konig's  law). 

Sensibility  to  slight  differences  in  wave- 
length has  two  pronounced  maxima  (one 
in  the  yellow,  one  in  the  green)  and  two 
slight  maxima  (extreme  blue,  extreme 
red). 

The  visual  sensation  as  a  function  of  the 
time  approaches  a  constant  value  with  the 
lapse  of  time.  With  blue  light  there 
seems  to  be  a  pronounced  maximum  at 
0.07  sec.,  with  red  a  slight  one  at  0.12  sec- 
onds, with  green  the  sensation  rises  stead- 
ily to  its  final  value.  For  lower  intensi- 
ties these  max.  occur  later. 

An  intensity  of  500  metre-candles  is  about 
that  on  a  horizontal  plane  on  a  cloudy 
day. 


SMITHSONIAN  TABLES. 


TABLES  159-162.    SOLAR  ENERGY.  179 

TABLE  159. —  Solar  Energy  and  Its  Absorption  by  the  Earth's  Atmosphere. 

The  following  values  depend  upon  the  formula  em  =  too.™,  where  em  is  the  observed  value  of  the 
solar  energy  after  transmission  through  a  mass  of  air,  m;  m  =  unity  when  the  sun  is  in  the  zenith, 
and  approximately=sec.  zenith  distance  for  other  positions  of  the  sun.  e0  =  the  energy  which 
would  have  been  observed  had  there  been  no  absorbing  atmosphere ;  a  is  the  amount  transmitted 
when  the  sun  is  in  the  zenith  or  when  m  =  i. 


Transmission  coefficient,  a. 

Intensity  of  Solar  Energy. 

• 
c 

j. 

jf 

Mt 

i* 

Wash- 

Mount 

JS 
>. 

|1 

Whit- 
ney. 

Mount  Wilson. 

Washington. 

rt 

ington. 

Wilson. 

•£    « 

<U     ^ 

£ 

5  B 

0 

o  $ 

^ 

a 

0.30 
•32 

- 

(485) 
(.562) 

.|22 
.61  s 

- 

95 

50 
1  2O 

46 
no 

22 
62 

05 
19 

1.2 
6.2 

- 

- 

- 

- 

- 

•34 

- 

.626 
676 

.687 
7  AC 

- 

305 

210 
11  T. 

191 

284 

120 

£ 

18 

- 

- 

- 

- 

- 

•38 

(.360) 

.713 

.788 

•SOS 

O1  J 

394 

3S7 

2SS 

129 

£ 

180 

6S 

23 

8 

I.I 

.40 

.46 

•  542 
•653 

.821 
.879 

.725 

580 
730 

476 
642 

433 

180 
323 

100 

477 

171 
3" 

92 

203 

5° 

15 

•50 
.60 

.704 
.762 

.850 
.884 

.902 
.942 

.829 
.862 

085 
590 

618 
SS6 

522 

495 
461 

360 

258 
281 

482 

340 
343 

239 
261 

199 

116 

.70 

•838 

-937 

.966 

.894 

454 

439 

425 

399 

3  So 

307 

380 

267 

224 

I57 

.80 

.867 

.981 

.909 

342 

336 

327 

312 

285 

260 

297 

257 

223 

i93 

i4S 

1.  00 

.901 

.968 

.991 

•930 

190 

1  88 

184 

178 

167 

ISO 

171 

IS4 

H9 

125 

1  02 

1.50 

2.00 

•923 
.909 

•977* 
.969* 

•956 
.925 

•95° 
•932 

82 
30 

28 

80* 
29* 

78* 
28* 

£ 

7'* 
25* 

76 
27 

70 
25 

64 
23 

60 

20 

17 

*  These  may  be  too  high  because  of  the  usual  increased  humidity  towards  noon  at  Mount  Wilson. 

TABLE  160.  -  Solar  Constant 

Solar  constant  (amount  of  energy  falling  at  normal  incidence  on  one  square  centimetre  per  min- 
ute on  body  at  earth's  mean  distance)  =  1.92  small  calories.  Mount  Wilson  and  Mount  Whitney 
observations. 

Computed  effective  temperature  of  the  sun :  Goldhammer's  method  (Ann.  der  Phys.  (4)  25, 
905,  1908),  6200°  Absolute  ;  from  form  of  black  body  curves,  6000  to  7000°  j  from  A.  max.  =  2930, 
6370° ;  from  Total  Radiation,  J  =  76.8X1  o~12,  5830°. 

TABLE  161.  -Distribution  of  Brightness  (Radiation)  over  the  Solar  Disk. 

(These  observations  extend  over  only  a  small  portion  of  a  sun-spot  cycle.) 


Wave-length 

0.323 

0.386 

0.433 

0.456 

0.481 

0.501 

0.534 

0.604 

V- 

0.670 

0.699 

0.866 

1.031 

1-225 

1.655 

2.097 

ro.oo 

144 

338 

4S6 

515 

5" 

489 

463 

399 

333 

307 

174 

III 

77-6 

39-S 

14.0 

(A 

0.40 

128 

312 

423 

486 

483 

463 

440 

382 

320 

109 

108 

75-7 

38.9 

13-8 

1 

K 

c  ' 

o-55 
0.65 

0.75 

120 
112 

289 
267 
240 

390 

456 
43° 
394 

437 
414 
38o 

396 

348 
326 

308 

295 
281 

273 
258 

I63 

'59 

T52 

105-5 
103 

99 

73-8 
72.2 
69.8 

38.2 
37-6 
36.7 

13-6 
13-4 
i3-i 

0.825 

86 

214 

296 

35i 

35» 

347 

337 

3°4 

262 

243 

94-5 

67.1 

3.5-7 

12.8 

g 

0.875 

76 

1  88 

266 

324 

323 

312 

284 

247 

229 

'So 

90.5 

64.7 

34-7 

12.5 

fa 

0.92 

64 

163 

233 

277 

290 

286 

281 

'259 

227 

212 

I30 

86 

61.6 

33-6 

12.2 

[0.95 

49 

141 

205 

242 

255 

254 

254 

237 

2IO 

195 

122 

81 

58.7 

32.3 

II.7 

TABLE  162.  — Relative  Distribution  in  Normal  Spectrum  of  Son  and  Sky-light  at  Mount  Wilson. 

Zenith  distance  about  50°. 




_.  .. 

/* 

M 

M 

I 

; 

C 

D 

b 

F 

Place  in  Spectrum 
Intensity  Sunlight 
Intensity  Sky-light 
Ratio  at  Mount  Wilson 
Ratio  computed  by  Rayleigh 
Ratio  observed  by  Rayleigh 

0.422 
186 
1194 
642 

0.457 
232 
986 
425 

0.491 
227 
701 
309 

0.566 

211 

0.6l4 

23I 
121 

0.660 

166 
174 
105 

25 
25 
25 

35 
40 

41 

60 
63 

71 

90 

Derived  from  vol.  II  and  unpublished  data  of  the  Astrophysical  Observatory  of  the  Smithsonian  Institution!  Abbot 
and  Fowle,  Astrophysical  Journal,  29,  1909,  and  Schwartzchild  and  Villiger,  same  Journal,  93,  1906. 

SMITHSONIAN  TABLES. 


180  TABLES  163-165.    INDEX  OF  REFRACTION  FOR  GLASS. 

TABLE  163.  -  Glasses  Made  by  Schott  and  Gen,  Jena. 

The  following  constants  are  for  glasses  made  by  Schott  and  Gen,  Jena :  »A,  «c»  «D»  nt>  nQ*  are 
the  indices  of  refraction  in  air  for  A=o.7682/t,  C  =0.6563/4,  0=0.5893,  F=o.486i,  G'=o.434i. 
v=(nv — I)/(«F — «c).  Ultra-violet  indices:  Simon,  Wied.  Ann.  53,  1894.  Infra-red:  Rubens, 
Wied.  Ann.  45,  1892.  Table  is  revised  from  Landolt,  Bornstein  and  Meyerhoffer,  Kayser,  Hand- 
buch  der  Spectroscopie,  and  Schott  and  Gen's  list  No.  751,  1909.  See  also  Hovestadt's  "Jena 
Glass." 


Catalogue  Type  = 

0546 

0381 

Oi84 

O  102 

Oi6S 

S57 

Designation     = 

Zinc-Crown. 

Higher  Dis- 
persion Crown. 

Light  Silicate 
Flint. 

Heavy  Silicate 
Flint. 

Heavy  Silicate 
Flint. 

Heaviest  Sili- 
cate Flint. 

Melting  N  umber  = 

1092 

1151 

45i 

469 

500 

163 

v            = 

60.7 

51.8 

41.1 

33-7 

27.6 

22.2 

Cd  0.2763/1 

•56759 

_ 

_ 

— 

— 

_ 

f 

Cd    .2837 
Cd    .2980 

•55723 

I-57093 

1-65397 

• 

— 

: 

Jl 

Cd    .3403 

•54369 

1.55262 

1.63320 

1.71968 

1.85487 

- 

> 

Cd    .3610 

•53897 

1.54664 

1.61388 

1.70536 

1.83263 

- 

m 

H      .4340/1 

•52788 

•533" 

•59355 

1.67561 

.78800 

1.94493 

•o 

H      .4861 

•52299 

•52715 

•58515 

1.66367 

.77091 

1.91890 

C    - 

Na    .5893 

.51698 

.52002 

•57524 

1.64985 

•75'30 

1.88995 

rt 

H      .6563 

.51446 

.51712 

•57"9 

1.64440 

•74368 

1.87893 

i 

K      .7682 

•5*  J43 

.51368 

.56669 

1.63820 

•73530 

1.86702 

J 

.800/1 

•5103 

<5I3X 

•5659 

I-6373 

•7339 

1.8650 

0 

1.200 

'.5048 

.5069 

•5585 

1.6277 

•7215 

1.8481 

C 

1.  600 

.5008 

.5024 

•5535 

1.6217 

.7151 

1.8396 

M 

2.000 

.4967 

•4973 

•5487 

1.6171 

.7104 

1.8316 

2.400 

•5440 

1.6131 

1.8286 

Percentage  composition  of  the  above  glasses  : 

O  546,  SiO2,  65.4;  K2O,  15.0;  Na2O,  5.0;  BaO,  9.6;  ZnO,  2.0;  Mn2O3,  o.i  ;  As2O3,  0.4; 

B203,  2.5. 

0381,  SiO2,  68.7;  PbO,  13.3;  Na2O,  15.7;  ZnO,  2.0;  MnO2,  o.i  ;  As2O5,  0.2. 
O  184,  SiO2,  53.7  ;  PbO,  36.0;  K2O,  8.3;  Na2O,  i.o;  Mn2O3,  0.06;  As2O8,  0.3. 

O  102,  SiO2,  40.0;  PbO,  52.6;  K2O,  6.5;  Na2O,  0.5;  Mn2O3,  0.09;  As2Os,  0.3. 

O  165,  SiO2,  29.26;  PbO,  67.5;  K2O,  3.0;  Mn2O3,  0.04;  As2O3,  0.2. 

S  57,     SiO2,  21.9;  PbO,  78.0;  As2O5,  o.i. 

TABLE  164. -Jena  Glasses. 


No.  and  Type  of  Jena  Glass. 

«„  for  D 

*D  —  I 

Specific 

O  225  Light  phosphate  crown     .     . 
O  802  Boro-silicate  crown  .... 
UV  3  199  Ultra-violet  crown   .    .     . 
O  227  Barium-silicate  crown  .     .     . 
O  1  14  Soft-silicate  crown   .... 
O  608  High-dispersion  crown      .    . 
UV  3248  Ultra-violet  flint  .     .    .     . 
0381  High-dispersion  crown      .    . 
O  602  Baryt  light  flint                    . 

i-5'59 
1.4967 
•5035 
•5399 
•SIS' 
.5149 
•5332 
.5262 
.1676 

.00737 
0765 
0781 
0909 
OgiO 
0943 
0964 
IO26 

70.0 
64.9 
64.4 

59-4 
56.6 
54-6 
55-4 
5i-3 

.00485 
0504 
0514 
0582 
0577 
°595 
0611 
0644 
0675 

.00515 

0534 
0546 
0639 
0642 
0666 
0680 
0727 

.00407 
0423 
0432 
0514 
0521 
0543 
0553 
0596 
0618 

2.58 
2-38 
2.41 
2-73 
2-55 
2.60 

2-75 
2.70 

5686 

M* 

51.6 

0712 

0629 

2.83 

O  726  Extra  light  flint        •          •     . 

e-iog 

0810 

0660 

2  87 

O  154  Ordinary  light  flint  .... 
O  184        "           "".... 

.5710 
.5900 
.6235 

1327 
M38 

43-0 
41.1 
39.1 

0819 
0882 
0965 

0943 

1022 
1142 

0791 
0861 
0065 

3.l6 
3.28 
3.67 

6480 

•jo.8 

1  1  80 

3  87 

041         "        "   

2434 

39*5 

1439 

1749 

1521 

4.49 

0  165       "        "  

27.? 

1607 

4.78 

S  386  Heavy  flint  .              ... 

2808 

.9626 

4882 

19.7 

2767 

3547 

3252 

6.33 

TABLE  165.  — Change  o<  Indices  of  Refraction  for  1°  0  In  Units  of  the  Fifth  Decimal  Place. 


No.  and  Designation. 

Mean 
Temp. 

C 

D 

F 

& 

—  A« 

100 
H 

S  57  Heavy  silicate  flint      .    .     . 

58.8° 

1.204 

1.447 

2.090 

2.810 

0.0166 

O  154  Light  silicate  flint     .    .    . 

58.4 

0.225 

0.261 

0-334 

0.407 

0.0078 

0327  Baryt  flint  light    .... 
O  225  Light  phosphate  crown     . 

58.3 
58.1 

—  0.008 

0.202 

0.014 
—  0.190 

0.080 
—o.i  68 

0.137 
—  0.142 

0.0079 
0.0049 

SMITHSONIAN  TABLES. 


Pulfrich,  Wied.  Ann.  45,  p.  609,  1892. 


TABLE  1 66. 
INDEX   OF   REFRACTION. 

Indices  of  Refraction  for  the  various  Alums.* 


0 

U 

Index  of  refraction  for  the  Fraunhofer  lines. 

R 

d 

g 

Q 

H 

a 

B 

c 

D 

E 

b 

P 

Q 

Aluminium  Alums,    J?Al(SO4)2+i2H2O.t 

Na 
NH3(CH3) 

1.667 
1.568 

17-28 
7-17 

1.43492 
•45OI3 

143563 
.45062 

I-43653 
•45I77 

1.43884 
.45410 

1.44185 
.45691 

1.44231 
•45749 

1.44412 
•45941 

1.44804 
•46363 

K 
Rb 
Cs 
NH4 

1-735 
1.852 
1.961 
1.631 

14-15 
7-21 

15-25 

15-20 

.45226 
45232 
•45437 
•45509 

•45303 
.45328 
•45517 
•45599 

•45398 
•45417 
.45618 

•45693 

.45645 
.45660 
.45856 
•45939 

•45934 
•45955 
.46141 
.46234 

•45996 
•45999 
.46203 
.46288 

.46181 
.46192 
.46386 
.46481 

.46618 
.46821 
•46923 

Tl 

2.329 

10-23 

.49226 

.493J7 

•49443 

.49748 

.50128 

.50209 

•50463 

.51076 

Indium  Alums.    -ff!n(SO4)2-|-i2H2O.t 

Rb 

2.065 

3-13 

1.45942 

1.46024 

1.46126 

1.46381 

1.46694 

1.467  Si 

I.46955 

1.47402 

Cs 

2.241 

17-22 

.46091 

.46170 

.46283 

.46522 

.46842 

.46897 

•47105 

.47562 

NH4 

2.OII 

17-21 

.46193 

.46259 

.46352 

.46636 

•46953 

-47015 

•47234 

•4775° 

Gallium  Alums.     /eGa(SO4)2-f  i2H2O.t 

Cs 
K 

2.II3 

I.89S 

17-22 

19~2S 

1.46047 
.46118 

1.46146 
.46195 

1.46243 
.46296 

1.46495 
.46528 

1.46785 
.46842 

1.46841 
.46904 

1.47034 
•47093 

1.47481 
.47548 

Rb 

1.962 

.46152 

.46238 

•46579 

.46890 

.46930 

.47126 

•4758i 

Tl 

1-777 
2.477 

15-21 
1  8-20 

.46390 
.50112 

.46485 
.50228 

•46575 
•50349 

:^! 

.47146 
•51057 

.47204 

.47412 
•51387 

.47864 
.52007 

Chrome  Alums.     *Cr(SO4)j-f  i2H2O.f 

Cs 
K 
Rb 

2.043 
1.817 
1.946 
1.719 

6-12 

6-17 

12-17 
7-18 

1.47627 
.47642 
.47660 
.47911 

1-47732 
.47738 
.47756 
.48014 

1.47836 
•47865 
.47868 
.48125 

1.48100 

-48137 
.48151 
.48418 

1.48434 

•48459 
.48486 
.48744 

1.48491 

•48513 
.48522 
.48794 

1.48723 
•48753 
•48775 
.49040 

1.49280 
.49309 
•49323 

Tl 

2.386 

9-25 

.51692 

•51798 

.52280 

.52704 

•52787 

•53082 

•53808 

Iron  Alums.    J?Fe(SO4)2+i2H,O.t 

K 
Rb 

i.  806 
1.916 

7-1  1 

7-20 

1.47639 

.47700 

1.47706 
.47770 

1.47837 
•47894 

1.48169 

.48234 

1.48580 
-48654 

1.48670 
.48712 

1.48939 
.49003 

1.49605 
.49700 

Cs 

2.061 

20-24 

•47825 

.47921 

.48042 

.48378 

.48797 

.48867 

.49136 

.49838 

NH4 

1.713 

7-20 

47927 

.48029 

.48150 

.48482 

.48921 

.48993 

.49286 

.49980 

Tl 

2-385 

15-17 

«5I674 

•S179° 

•5I943 

-52365 

.52859 

.52946 

.53284 

.54112 

*  According  to  the  experiments  of  Soret  (Arch.  d.  Sc.  Phys.  Nat.  Geneve,  1884,  1888,  and  Comptes  Rendus,  1885). 
t  R  stands  for  the  different  bases  given  in  the  first  column. 

SMITHSONIAN  TABLES. 


182 


TABLE  167. 
INDEX  OF  REFRACTION. 

Index  of  Refraction  of  Metals  and  Metallic  Oxides. 


(a)  Experiments  of  Kundt  *  by  transmission  of  light  through  metallic  prisms  of  small  angle. 

Name  of  substance. 

Index  of  refraction  for 

Red. 

White. 

Blue. 

Silver 

0.38 

045 
I.76 
1.81 
2.17 
2.61 
1.04 
0.89 

1.78 
2.18 
2.63 

4-99 

0.27 
0.58 
0.65 
1.64 

2.01 
2.26 

0.99 
2.03 
I.9I 
2.1  1 
2.23 
2.84 

3-29 
4.82 

1.  00 

•44 

•13 

.25 

•33 

2.36 
2-39 

2.90 
4.40 

Gold 

Nickel 

Gold  and  gold  oxide 

«              «        «   -j- 
Bismuth  oxide  . 
Iron  oxide         .        .        •  ' 

•          •          i 

Copper  oxide 

Platinum  and  platinum  oxide  . 

(V)  Experiments  of  Du  Bois  and  Rubens  by  transmission  of  light  through  prisms  of  small  angle. 

The  experiments  were  similar  to  those  of  Kundt,  and  were  made  with  the  same  spectrometer. 
Somewhat  greater  accuracy  is  claimed  for  these  results  on  account  of  some  improvements  intro- 
duced, mainly  by  Prof.  Kundt,  into  the  method  of  experiment.     There  still  remains,  however, 
a  somewhat  large  chance  of  error. 

Name  of  metal. 

Index  of  refraction  for  light  of  the  following  color  and  wave-length. 

Red(Lia). 
A  =  67.1 

"Red." 
A  =  64.4 

Yellow  (D). 
A  =58-9 

Blue  (F). 

A  =  48.6 

Violet  (G). 
A  =  43.1* 

Nickel     . 
Iron 
Cobalt     . 

2.04 
3.12 
3-22 

3-10 

1.84 

2.72 
2.76 

I.7I 

2-43 
2-39 

i-54 

2.05 

2.10 

(0)  Experiments  of  Drude. 

The  following  table  gives  the  results  of  some  of  Drude's  experiments.  §    The  index  of  refrac- 
tion is  derived  m  this  case  from  the  constants  of  elliptic  polarization  by  reflection,  and  are  for 
sodium  light. 

Metal. 

£S£ 

Index  of 
refraction. 

Aluminium 
Antimony 
Bismuth 
Cadmium 
Copper    . 
Gold        . 
Iron 
Lead 
Magnesium 

1.44             Mercury 
3.04             Nickel     . 
1.90             Platinum 
1.13             Silver 
0.641           Steel 
0.366           Tin,  solid 
2.36               "    fluid 
2.01             Zinc 
0-37 

i-73 
1.79 
2.06 
0.181 
2.41 
1.48 

2.10 
2.12 

*  "  Wied.  Ann."  vol.  34,  and  "  Phil.  Mag."  (5)  vol.  26.                         t  Nearly  pure  oxide, 
t  Wave-lengths  A  are  in  millionths  of  a  centimetre.                                 §  "  Wied.  Ann."  vol.  39. 

SMITHSONIAN  TABLES.                                                              s 

TABLES  168-170.    INDEX  OF  REFRACTION, 
TABLE  188.  -Index  of  Refraction  of  Rock  Salt  in  Air. 


MM). 

«. 

Obser- 
ver. 

MM). 

n. 

Obser- 
ver. 

M,). 

n. 

Obser- 
ver. 

0.185409 

1.89348 

M 

0.88396 

I.5340II 

L 

5-8932 

1.516014 

P 

.204470 
.291368 

1.76964 
I.6I325 

« 

.972298 
.98220 

1-532532 
1-532435 

H 

P 

«< 
6.4825 

I-5I5553 
1.513628 

L 
P 

.358702 

L57932 

" 

1.036758 

1.531762 

L 

" 

I.5I3467 

L 

.441587 

1.55962 

« 

1.1786 

1.530372 

P 

7.0718 

1.511062 

P 

.486149 

L55338 
1.553406 

L 

I.555I37 

I.530374 
1.528211 

L 

7.66II 
7-9558 

1.508318 
1.506804 

« 

M 

J-553399 

P 

1.7680 

1.527440 

P 

8.8398 

1.502035 

.58902 

1.544340 

L 

M 

1.527441 

L 

IO.OI84 

1.494722 

•58932 
•656304 

I.5443I3 
1.540672 

P 
P 

2.073516 
2.35728 

1.526554 
1.525863 

P 

11.7864 
I2.965O 

1.481816 
1.471720 

" 

1.540702 

L 

1.525849 

L 

14.1436 

1.460547 

.706548 

1-538633 

P 

2.9466 

1.524534 

P 

14.7330 

1.454404 

.766529 

1.536712 

P 

3-5359 

1.523173 

" 

15.3223 

1.447494 

.76824 

1.53666 

M 

4.1252 

1.521648 

P 

I5.9II6 

1.441032 

.78576 

1.536138 

P 

1.521625 

L 

20-57 

L3735 

RN 

.88396 

i  -53401  1 

P 

5.0092 

I.5I8978 

P 

22.3 

1.340 

where  az=  2.330165 
MI  =0.0127868  5 
Ax2  =0.0  1  48  500 
^2=0.005343924 


A2a=  0.02  54741  4 
£=0.00092858 
>&=  0.00000028 


£2=5.680137 
Ms=  12059.95 
A32=36oo.  ' 


(P) 


TABLE  169.—  Change  of  Index  of  Refraction  for  1°  C  in  Units  of  the  5th  Decimal  Place. 


O.2O2,l 

+3-134 

Mi 

0.441,4 

—3-425 

Mi 

C  line 

—3-749 

PI 

0.760,, 

—3-73 

L 

.2IO 

+  1-570 

.508 

—  3-5T7 

" 

D    " 

—3-739 

" 

1.368 

—3-88 

L 

.224 

* 

•643 

—3-636 

M 

p    « 

-3-648 

14 

1.88 

-3-85 

L 

.2Q8 

—2.727 

« 

G'  " 

-3-585 

« 

4-3 

-3-82 

L 

L    Annals  of  the  Astrophysical   Observatory 
of  the  Smithsonian  Institution,  Vol.  I,  1900. 
M   Martens,  Ann.  d.  Phys.  6,  1901,  8,  1902. 
Mi  Micheli,  Ann.  d.  Phys.  7,  1902. 


P  Paschen,  Wied.  Ann.  26,  1908. 
PI  Pulfrich,  Wied.  Ann.  45,  1892. 
RN  Rubens  and  Nichols,  Wied.  Ann,  60, 1897. 


TABLE  170.- Index  of  Refraction  of  Silvine  (Potassium  Chloride)  in  Air. 


MM). 

n 

Obser- 
ver. 

MM). 

n. 

Obser- 
ver. 

MM). 

n. 

Obser- 
ver. 

0.185409 

1.82710 

M 

1.1786 

1.478311 

P 

8.2505 

1.462726 

P 

.200090 

1.71870 

" 

1.47824 

W 

d 

1.46276 

W 

.21946 

1.64745 

1.7680 

1.475890 

P 

8.8398 

1.460858 

p 

•237317 

1.58125 

" 

1.47589 

W 

" 

1.46092 

W 

.281640 

I-55836 

2.35728 

I.474751 

p 

10.0184 

1.45672 

p 

.308227 

I.54I36 

2.9466 

1.473834 

« 

« 

I-45673 

W 

.358702 

I.52H5 

" 

1-47394 

W 

11.786 

1.44919 

p 

.394415 

1.51219 

3-5359 

1.473049 

p 

« 

1.44941 

W 

.467832 

1.50044 

M 

1.47304 

W 

12.965 

1.44346 

p 

.508606 

1.49620 

47146 

1.471122 

p 

<4 

1.44385 

W 

.58932 

1.490443 

P 

« 

1.47129 

W 

14.144 

1.43722 

p 

.67082 

1.48669 

M 

5-3039 

1.470013 

p 

15.912 

1.42617 

«( 

.78576 

1.483282 

P 

1.47001 

W 

17.680 

1.41403 

« 

.88398 

1.481422 

P 

5-8932 

1.468804 

p 

20.00 

1.3882 

RN 

.98220 

1.480084 

M 

1.46880 

W 

22.5 

1.369 

«   : 

«2="2+  ^±i+^±*-**-'<*  or=*2+  re 


a2=2.  174967 
Ml^=  0.008344206 
Ai2=o.oi  19082 
^2=0.00698382 

W  Weller,  see  Paschen's  article.    Other  references  as  under  Table  169,  above. 
SMITHSONIAN  TABLES. 


£=0.000513495 
h  =0.000000  1  67  587 


£2=3.866619 
^3=5569.715 
A32=3292.47  (P) 


1 84 


TABLES  171-174. 
INDEX  OF  REFRACTION. 

TABLE  171.  —  Index  of  Refraction  of  Fluorite  in  Air. 


AGO 

m 

Obser- 
ver 

A  00 

» 

Obser- 
ver 

*GO 

n 

Obser- 
ver. 

0.1856 
.19881 

1.50940 
1.40629 

S 

14733 
'I71! 

1.42641 

1.42596 

P 

« 

4.1252 
4.4199 

1.40855 
1.40559 

P 

« 

.21441 

1.48462 

M 

1.6206 

1.42582 

« 

4.7146 

1.40238 

« 

.22645 

1.47762 

U 

1.7680 

1.42507 

«« 

5.0092 

1.39898 

« 

•25713 
•32525 

1.46476 
1.44987 

(t 

u 

'WS 

1.9644- 

1.42437 
1.42413 

M 

« 

5-3036 
5-5985 

1.39529 
1.39142 

« 
<( 

•34555 

1.44697 

N 

2.0626 

142359 

« 

5-8932 

1.38719 

« 

•39®' 

1.44214 

|| 

2.1608 

1.42308 

«« 

6.4825 

1.37819 

ft 

.48607 

I437I3 

P 

2.2IOO 

1.42288 

«« 

7.0718 

1.36805 

M 

•5893° 

143393 

p 

2-3573 

1.42199 

« 

7.6612 

1.35680 

«« 

.65618 

I43257 

S 

2-5537 

1.42088 

« 

8.2505 

1.34444 

«i 

.68671 

1.43200 

« 

2.6519 

1.42016 

« 

8.8398 

1  -33079 

« 

.71836 

I43I57 

n 

2.7502 

1.41971 

M 

9.4291 

1.31612 

" 

.76040 
.8840 

1.43101 

1.42982 

« 
P 

2.9466 

3-M30 

1.41826 
1.41707 

M 

I1'2 
61.  i 

347 
2.66 

RA 

« 

1.1786 

1.42787 

" 

3-2413 

1.41612 

" 

00 

2.63 

S 

1.17  $6 

1.42690 

u 

•5   CT  CO 

I  d.1  "37Q 

« 

O/  J 

M733 

1.42641 

u 

•J'  jo  jV 

3.8306 

'•M-1  j/y 
I.4II20 

« 

References  under  Table  173. 

—  "+^-* *-/*<°r=^^ 


where  a2  =  2.03882 
^/i  =  0.0062 1 83 
Ai2  =  0.007  706 
<?  =  0.0031999 


/=  0.0000029 1 6 
p  =  6.0965 1 
1/2  =  0.0061386 
^  =  0.00884 


1=5114.65 

Ar2=i26o.56 
At,  =  0.0940^ 


(P) 


TABLE  172. —  Change  of  Index  of  Refraction  for  1°0  in  Units  of  the  5th  Decimal  Place. 
C  line, —1.220;  D,  —1.206;  F,  —1.170;  G,  —1.142.     (PI) 

TABLE  173. -Index  of  Refraction  of  Iceland  Spar  (CaC03)  in  Air. 


A  (ju.) 

* 

n. 

Obser- 
ver. 

AGO 

n0 

* 

Obser- 
ver. 

AW 

n0 

nt 

Obser- 
ver. 

0.198 

_ 

1.5780 

M 

0.508 

1.6653 

1.4896 

M 

0.991 

1.6438 

1.4802 

C 

.2OO 
.208 
.226 

1.9028 
1.8673 
1.8130 

'•57j>5 
1.5664 
1.5492 

u 
It 

•533 

1*6584 

1.6550 

1.4884 
1.4864 
1.4849 

H 

.229 
•3°7 

-497 

L6393 
1.6346 

1.4787 
14783 
1-4774 

«« 

.298 

1.7230 
1.7008 

I.5056 

C 
M 

.656 
.670 

1.6544 
'•6537 

1.4846 
1.4843 

M 

.682 
-749 

1-6313 

1.4764 

« 

.361 

1.6932 

1.5022 

C 

.760 

1.6500 

1.4826 

- 

.849 

1.6280 

N 

.410 

1.6802 

1.4964 

— 

.768 

1.6497 

1.4826 

M 

.908 

_ 

M757 

'« 

434 

1.6755 

1-4943 

M 

.801 

1.6487 

1.4822 

C 

2.172 

1.6210 

« 

.486 

1.6678 

1.4907 

•905 

1.6458 

1.4810 

2.324 

I 

14739 

U 

C    Carvallo,  J.  de  Phys.  (3),  9,  1900. 

M   Martens,  Ann.  der  Phys.  (4)  6,  1901,  8,  1902. 

P    Paschen,  Wied.  Ann.  56,  1895. 


PI      Pulfrich,  Wied.  Ann  45,  1892. 

RA   Rubens-Aschkinass,  Wied.  Ann.  67,  1899. 

S       Starke,  Wied.  Ann.  60,  1897. 


TABLE  174.— Index  of  Refraction  of  Nltroso-dlmethyl-anlline.    (Wood.) 


A 

n 

A 

n 

A 

n 

A 

n 

A 

n 

0.497 

2.140 

0.525 

1-945 

0.584 

.815 

0.636 

1.647 

o-7  13 

1.718 

.500 

2.114 

.536 

1.909 

.602 

.796 

.647 

1.758 

•730 

I.7I3 

.506 

2.074 

1.879 

.611 

.783 

1-75° 

•749 

1.709 

.508 
.516 

2.025 
1.985 

$ 

1.857 
1.834 

.620 
.627 

.778 
.769 

^696 

1-743 
1-723 

•763 

1.697 

Nitroso-di methyl-aniline  has  enormous  dispersion  in  yellow  and  green,  metallic  absorption  in  violet.    See  Wood, 

Phil.  Mag.  1903. 


SMITHSONIAN    TABLES. 


TABLE  1  75. 
INDEX  OF  REFRACTION. 

Index  of  Refraction  of  Quartz  (SiOz). 


i8S 


Wave- 
length. 

Index 
Ordinary 
Ray. 

Index 
Extraordinary 
Ray. 

Tempera- 
ture  °  C. 

Wave- 
length. 

Index 
Ordinary 
Ray. 

Index 
Extraordinary 
Ray. 

Tempera- 
.ture  °  C. 

0.185 
.193 
.198 

1.67582 

.65997 
.65090 

1.68999 

•67343 
.66397 

18 

0.656 
.686 
.760 

1.54189 
.54099 
•539I7 

1.55091 
.54998 
.54811 

18 

M 

.206 

.64038 

.65300 

1.160 

.5329 

— 

.214 

.63041 

.64264 

.969 

.5216 

- 

.219 

.62494 

.63698 

2.327 

•5I56 

— 

.231 

•61399 

.62560 

.84 

•5°39 

— 

•257 

.59622 

.60712 

3.18 

•4944 

— 

.274 

.58752 

.59811 

•4799 

1-  Rubens. 

_ 

•340 

.56748 

.57738 

.96 

.4679 

— 

.396 

•55815 

.56771 

4.20 

•4569 

- 

.410 

•55650 

.56600 

" 

5-° 

.417 

— 

.486 

.54968 

.55896 

" 

6.45 

.274 

— 

0.598 

1.54424 

1-55334 

7.0 

1.167 

t 

Except  Rubens'  values,  —  means  from  various  authorities. 
SMITHSONIAN  TABLES. 


1 86 


TABLE  176. 
INDEX   OF   REFRACTION. 

Various  Monorefrlngent  or  Optically  Isotropic  Solids. 


Substance. 

Line  of 
Spectrum. 

Index  of 
Refraction. 

Authority. 

red 

I.C-J.74 

De  Senarmont. 

D 

I.O422 

Grailich 

Arsenite      

D 
D 

1-755 
i.c^io 

DesCloiseaux. 
Fock. 

Bell  metal           

D 

1.0052 

Beer. 

Blende        

Li 

Na 

2-34165  J 
2.36027  > 

Ramsav. 

Boric  acid           

Tl 
C 
D 

fj  \ 

2.40069  ) 

1.46245 
1.46701 

Borax  (vitrified)          

F 
C 
D 

1.47024 
1.51222 
1.51484 

Bedson  and 
Carleton  Williams. 

F 
D 

1.52068 
1  I<532 

Kohlrausch. 

Diamond  (colorless)  

(red 

(  1-5462 
2.414 

Mulheims. 
DesCloiseaux. 

}  green 
(B 
<D 

2.428 
2.46062 
2.46086 

Schrauf 

Ebonite      . 

*l 

2.47902 
1.6 

Ayrton  &  Perry. 

A 
B 

2.03 
2.19 

2  -3  -3 

Means 

Garnet  (different  varieties)        .        •       « 

G 
H 

D 

red 

*'JJ 
1.97 
1.32 

(  1.74  to 

1  1-90 

I  480 

Various. 
Tamin 

««        « 

H 

I.CI4 

Wollaston. 

D 

»*3»5 

1.4061 

Tschichatscheff. 

D 

1.7-30 

Levy  &  Lecroix. 

Obsidian     

D 

(  i.  482  to) 

Various. 

Opal   . 

D 

1  1.496    1 

1.406 

« 

Pitch           

red 

(  !45°     ) 
i.fJli 

Wollaston. 

D 

l.ccqi    ) 

"          chlorstannate    .... 

« 
« 

jjyj    i 
1.6574    \ 
1.6666    ) 

Topsoe  and 
Christiansen. 

« 

2.1442 

Gladstone  &  Dale. 

red 

1.619 

Jamin. 

Canada  balsam     .... 

u 

(t 

1.528 
1.548 

Wollaston. 
Jamin. 

Copal    

<« 

1.528 

Mastic  
Peru  balsam         .... 

« 

D 
fA 

IB 

1-535 
1-593 
2.612     ) 
2.680 

Wollaston. 
Baden  Powell. 

Wood. 

1  c 

{% 

2.729 
2-93       J 

2.2ZT. 

« 

2  061 

Wernicke 

(  iodide     

ti 
« 

2.182 
1.4827 

Sodallte  |  clear  like  water         ... 

« 

« 

14833 
j.ci  en 

Feusner. 
Dussaud. 

« 

I.7I  5C 

DesCloiseaux. 

« 

**/*3J 

I.c66? 

Fock. 

SMITHSONIAN  TABLES. 


TABLES  177,  178. 
INDEX   OF   REFRACTION. 

TABLE  177.  -Uniaxial  Crystals. 


i87 


Substance. 

Line  of 
spec- 
trum. 

Index  of  refraction. 

Authority. 

Ordinary 
ray. 

Extraordi- 
nary ray. 

D 
red 
D 
D 
D 

v 

red 
red 

red  j 

green 
green 
D 

1* 

D 
red 
red 
red 
D 
D 
D 
D 
D 
D 

DJ 

red 
D 

'•573 

1-577 

2-5354 
1.6390 
1.6588 
1.589  to 
1-570 
1.560 
1.96 
2.854 
1.767  to 

1.769 
1.667 
1.584 
1.309 

1.719  to 

1.722 

*-539 

1.717 
1.564 

M93 

1459 
1.587 
1.446 
1.614 
1.997 
1-637 
1.633  to 
1.650 
1.92 
1.924 

1.592 

4-524 
2.4959 
1-6345 
1.6784 
1.582  to 
1.566 

«•£« 

2.60 

3-199 

1-759 
1.762 
1.723 
1-573 

I-3I3 
1.717  to 
1.720 
i-54i 
I-5I5 
i-5i5 
1.501 
2.881 
1.467 
J-336 
2.452 

i-5i9 

2.093 
1.619 
1.616  to 
1.625 
1.97 
1.968 

Levy  &  Lacroix. 
De  Senarmont. 

Schrauf. 

« 

DesCloiseaux. 
f  Various. 

Kohlrausch. 
De  Senarmont. 
DesCloiseaux. 

1 

M 
«« 

Meyer. 
£  DesCloiseaux. 

Kohlrausch. 
Mallard. 
DesCloiseaux. 
De  Sernamont. 
Fizeau. 
Baker. 
Schrauf. 
Dufet. 
Martin. 
Grubenman. 
Heusser. 

}  Jerofejew. 

De  Senarmont. 
Sanger. 

Benzil  

Beryl    ........ 

Calomel       ....... 

Corundum  (ruby,  sapphire,  etc.)         . 

Ice  at       8°  C       

«                « 

Sodium  arseniate         

Strychnine  sulphate     .        .         .        . 

Tourmaline  (colorless)        .... 
"          (different  colors)     . 

«              « 

TABUS  178.—  Biaxial  Crystals. 


Substance. 

Line  of 
spec- 
trum. 

Index  of  refraction. 

Authority. 

Minimum. 

Interme- 
diate. 

Maximum. 

Anglesite 

D 

1.8771 

1.8.823 

1.8936 

Arzruni. 

Anhydrite     . 
Antipyrin 

D 
D 

1.5693 
I.5IOI 

1-5752 
I.68I2 

1.6130 
1.6858 

Mulheims. 
Glazebrook. 

Aragonite     . 
Axinite 

D 

red 

I-530I 
1.6720 

1.6816 
1.6779 

1.6859 
I.68IO 

Rudberg. 
DesCloiseaux. 

Barite   .... 

D 

1.636 

1.648 

Various. 

Borax  .... 

D 

1.4467 

1.4694 

1.4724 

Dufet. 

Copper  sulphate  . 
Gypsum 

D 
D 

1.5140 

1.5208 

1-5368 

1.5228 

1-5433 
1.5298 

Kohlrausch. 
Mulheims. 

Mica  (muscovite)  . 

D 

I  5601 

1.5936 

1-5977 

Pulfrich. 

Olivine  .... 

D 

I.66I 

1.678 

1.697 

DesCloiseaux. 

Orthoclase    . 
Potassium  bichromate  . 

D 
D 

I.5I90 

1.7202 

i.5237 
1.7380 

1.5260 
1.8197 

<{ 
Dufet. 

"         nitrate 

D 

13346 

1-5056 

1.5064 

Schrauf. 

"         sulphate 

D 

1-4932 

1.4946 

1.4980 

Topsoe  &  Christiansen. 

Sugar  (cane) 

D 

!-5397 

1.5667 

1.5716 

C  alder  on. 

Sulphur  (rhombic) 

D 

I-9505 

2.0383 

2.2405 

Schrauf. 

Topaz  (Brazilian) 

D 

1.6294 

1.6308 

J-6375 

Mulheims. 

Topaz  (different  kinds) 

Dl 

1.630  to 
1.613 

1.631  to 
1.616 

1.637  to 
1.623 

>  Various. 

Zinc  sulphate 

D 

1.4568 

1.4801 

1.4836 

Topsoe  &  Christiansen. 

SMITHSONIAN  TABLES. 


188 


TABLE  179. 
INDEX  OF  REFRACTION. 

Indices  of  Refraction  relative  to  Air  for  Solutions  of  Salts  and  Acids. 


Substance. 

Indices  of  refraction  for  spectrum  ines. 

Authority. 

Density. 

Temp.  C 

D 

0 

P 

Hy 

H 

(a)  SOLUTIONS  IN  WATER. 

Ammonium  chloride 

1.067 

27°.os 

1.37703 

1.37936 

L38473 

L39336 

Willigen. 

.025 

2975 

.34850 

.35050 

-355r5 

•36243 

M 

Calcium  chloride 

•398 

25-65 

44000 

.44279 

•44938 

46001 

• 

" 

* 

•215 

22.9 

•39411 

.39652 

40206 

.41078 

* 

•143 

25.8 

•37152 

.37369 

•37876 

.38666 

1 

Hydrochloric 
Nitric  acid  . 

acid    . 

I.I66 

•359 

20.75 
18.75 

1.40817 

•39893 

141109 
.40181 

141774 
40857 

1.42816 
41961 

H 

Potash  (caustic)  .    . 

.416 

1  1.0 

40052 

40281 

.40808 

41037 

Fraunhofer. 

Potassium  chloride  . 

normal  solution 

.34087 

•34278 

•34719 

I.35049 

Bender. 

" 

" 

double  normal 

.34982 

•35*79 

•35645 

•35 

994 

1 

M 

" 

triple  normal 

•35831 

.36029 

•36 

512 

.36 

*90 

" 

Soda  (caustic)      .    . 
Sodium  chloride  .     . 

1.376 
.189 

21.6 

18.07 

141071 

.37562 

1413 

•377 

34 
^ 

141936 

•38322 

1.38746 

1.42872 

Willigen. 
Schutt. 

" 

• 

.109 

18.07 

•35751 

•35959 

•36442 

•36823 

H 

•035 

18.07 

.34000 

•34191 

•34628 

.34969 

Sodium  nitrate     .    . 
Sulphuric  acid      .    . 

'Ifl 

22.8 
18-3 

1.38283 
-43444 

1-385 
436 

35 

I.39I34 
44168 

- 

140121 
44883 

Willigen. 

.632 

I8.3 

42227 

42466 

42967 

43694 

" 

" 

.221 

I8.3 

•36793 

•37009 

.37468 

•38 

1  1;8 

" 

« 

.028 

I8.3 

•33663 

.33862 

•34285 

- 

•34938 

Zinc  chloride   .    .    . 

*-359 

26.6 

1-39977 

140222 

140797 

141 

738 

•    •    • 

.209 

264 

.37292 

•37515 

.38026 

•38 

*45 

(b)  SOLUTIONS  IN  ETHYL 

ALCOHOL. 

Ethyl  alcohol  .     .    . 

0.789 
•932 

25-5 
27.6 

I-3579I 

•35372 

i.3597i 
•35556 

1.36 
•35 

395 
#6 

- 

'•37094 
.36662 

Willigen. 

Fuchsin  (nearly  sat- 

urated)    . 

• 

_ 

16.0 

.3918 

•398 

•36 

•3759 

Kundt. 

Cyanin  (saturated)   . 

- 

1  6.0 

.3831 

•3705 

•3821 

" 

NOTE.  —  Cyanin  in  chloroform  also  acts  anomalously  ;  for  example,  Sieben  gives  for 

a  4.5  per  cent,  solution  VLA=  14593,  /*B=  14695,  juj-(green)  =  I45I4>  /*<?  (blue)  =  14554. 
For  a  9.9  per  cent,  solution  he  gives  HA—  14902,  /i/?(green)  =  14497,  /to  (blue)  =  14597. 

(c)  SOLUTIONS  OF  POTASSIUM  PERMANGANATE  IN  WATER.* 

Wave- 
length 

Spec- 
trum 

Index 
for 

Index 
for 

Index 
for 

Index 
for 

Wave- 
length 

Spec- 
trum 

Index 
for 

Index 
for 

Index 
for 

Index 
for 

X  io6. 

line. 

I  %  SOI. 

2  %  sol. 

3%  sol. 

4  %  sol. 

in  cms. 
Xio6. 

line. 

I  %  SOI. 

2%  sol. 

3  %  sol. 

4  %  sol. 

68.7 

B 

1.3328 

1-3342 

_ 

L3382 

Si.  6 

_ 

L3368 

L3385 

_ 

_ 

65.6 

C 

•3335 

•3348 

L3365 

•3391 

5°.° 

- 

•3374 

•3383 

1.3386 

1.3404 

6l.7 

— 

•3343 

•3365 

.3381 

.3410 

48.6 

F 

•3377 

.3408 

594 

- 

•3354 

•3373 

•3393 

.3426 

48.0 

- 

•3381 

•3395 

•3398 

•3413 

58.9 

D 

•3353 

•3372 

.3426 

46.4 

— 

•3397 

.3402 

.3414 

.3423 

56.8 

— 

.3362 

•3387 

.3412 

•3445 

44-7 

— 

•3407 

•3421 

.3426 

•3439 

55-3 
52-7 

E 

•3366 
•3363 

•3395 

•3417 

•3438 

434 
42.3 

_ 

.3417 
•343  1 

•3442 

•3457 

•3452 
•3468 

52.2 

•3362 

•3377 

.3388 

" 

" 

SMITHSONIAN  TABLES. 


According  to  Christiansen. 


TABLE  180. 

INDEX   OF   REFRACTION. 

Indices  of  Refraction  of  Liquids  relative  to  Air. 


189 


Substance. 

Temp. 

Index  of  refraction  for  spectrum  lines. 

Authority. 

0 

D 

P 

Hr 

H 

Acetone     .... 

10° 

1.3626 

1.3646 

1.3694 

I-3732 

_ 

Korten. 

Almond  oil    ... 

0 

4755 

.4782 

.4847 

_ 

Olds. 

Analin*     .... 
Aniseed  oil    ... 

20 
21.4 

•5993 
.5410 

.5863 
•5475 

.6041 
•5647 

.6204 

: 

Weegmann. 
Willigen. 

«             u 

IS-I 

•55o8 

•5572 

•5743 

- 

1.6084 

Baden  Powell. 

Benzene  t  •     •    •    • 

10 

1.4983 

1.5029 

1.5148 

_ 

1.5355 

Gladstone. 

Bitter  almond  oil    . 
Bromnaphtalin   .     . 

21.5 
2O 
20 

4934 
•5391 
.6495 

4979 
.6582 

•5095 
•5623 
.6819 

•5775 
.7041 

•53°4 
.7289 

Landolt. 

Walter. 

Carbon  disulphide  J 

0 

1.6336 

I-6433 

1.6688 

1.6920 

I-7I75 

Ketteler. 

«              « 

2O 

.6182 

.6276 

•6523 

.6748 

.6994 

« 

««              « 

IO 

.6250 

•6344 

.6592 

.7078 

Gladstone.  ' 

«              « 

J9 

.6189 

.6284 

•6352 

_ 

.7010 

Bufet. 

Cassia  oil  .    .    .     . 

IO 

.6007 

.6104 

•6389 

_ 

•7°39 

Baden  Powell. 

"       "   .    .     .    . 

22.5 

•593° 

.6026 

.6314 

- 

«          « 

Chinolin    .... 

20 

1.6094 

1.6171 

1.6361 

1.6497 

_ 

Gladstone. 

Chloroform    .    .    . 

IO 

.4466 

.4490 

4555 

.4661 

Gladstone  &  Dale. 

"            ... 

3° 

— 

4397 

— 

456i 

«               « 

.... 

20 

4437 

.4462 

4525 

_ 

Lorenz. 

Cinnamon  oil     .    . 

23-5 

.6077 

.6188 

.6508 

- 

- 

Willigen. 

Ether     

15 

'•3554 

1.3566 

1.3606 

_ 

1-3683 

Gladstone  &  Dale. 

« 

T  r 

•JC77 

-J  CQA 

i6di 

_ 

•771-1 

Kundt. 

Ethyl  alcohol      .     . 

O 

0 

•J57J 
•3677 

•ojy^ 
•3695 

•j^1 
•3739 

•3773 

•o/1  o 

Korten. 

«           « 

IO 

•3636 

•3654 

•3698 

•3732 

— 

« 

«           « 
«           «« 

20 

15 

•3596 
.3621 

.3614 
•3638 

•3657 
•3683 

.3690 

•3751 

Gladstone  &  Dale. 

Glycerine  .... 

20 

1.4706 

_ 

1.4784 

1.4828 

_ 

Landolt 

Methyl  alcohol  .     . 
Olive  oil    .... 

15 

o 

.3308 
4738 

1.3326 
4763 

•3362 
4825 

— 

.3421 

Baden  Powell. 
Olds. 

Rock  oil    .... 

o 

4345 

4573 

4644 

— 

— 

M 

Turpentine  oil    .     . 

10.6 

I47I5 

1.4744 

1.4817 

- 

14939 

Fraunhofer. 

«           « 
Toluene     .... 

20.7 
20 

.4692 
.4911 

.4721 
4955 

4793 
.5070 

Wo 

49  i  3 

Willigen. 
Bruhl. 

Water§      .    .    .    . 

20 

•3312 

•333° 

•3372 

•3404 

•3435 

Means. 

*  Weegmann  gives  pD=  1.59668  —  .000518*.  Knops  gives  HF—  1.61500—  .00056*. 
t  Weegmann  gives  HD  =  1.51474  —  .000665*.  Knops  gives  HD=  1.51^9  —  .000644*. 
$  Wiillner  gives  MC=  1.63407  —  .00078*;  /*/•=  1.66908  —  .00082  *;  nh  =  1.6921$—  .00085*. 


§  Dufet  gives  HD=  1.33397—  io~7  (125*  +  20.6  **  —  .000435  P  —  .00115**)  between  o°  and  50°;  and  nearly  the 
same  variation  with  temperature  was  found  by  Ruhlmann,  namely,  ^=1.33373  —  io~7  (20.  14**  +  .000494**). 

SMITHSONIAN  TABLES. 


190  TABLE  181. 

INDEX   OF  REFRACTION. 

Indices  of  Refraction  of  Gases  and  Vapors. 

A  formula  was  given  by  Biot  and  Arago  expressing  the  dependence  of  the  index  of  refraction  of  a  gas  on  pressure  and 
temperature.  More  recent  experiments  confirm  their  conclusions.  The  formula  is  nt—i  =  n°7^\-4-t  where 
nt  is  the  index  of  refraction  for  temperature  f,  «0  for  temperature  zero,  a  the  coefficient  of  expansion  of  the  gas 
with  temperature,  and>  the  pressure  of  the  gas  in  millimetres  of  mercury.  Taking  the  mean  value,  for  air  and 
white  light,  of  n0  —  i  as  0.0002936  and  a  as  0.00367  the  formula  becomes 

n  —  i—    .0002936      .  P  . 

i  -f- -00367*     1.0136  X  io8 


.0002  _ 

i  -f-  .00367  ioe' 


where  P  is  the  pressure  in  dynes  per  square  centimetre,  and  t  the  temperature  in  degrees  Centigrade. 


(a)  The  following  table  gives  some  of  the  values  obtained  for  the  different  Fraunhofer  lines  for  air. 

Spectrum 
line. 

Index  of  refraction  according  to  — 

Spec.™       M£*S*«i» 
Kayser  &  Runge. 

Ketteler. 

Lorenz. 

Kayser  &  Runge. 

A 
B 
C 
D 
E 

F 
G 
H 
K 
L 

1.0002929 

2935 
2938 
2947 
2958 

1.0002968 
2987 

3°°3 

1.0002893 
2899 
2902 
2911 
2922 

1.0002931 
2949 
2963 

1.0002905 
2911 
2914 
2922 
2933 

1.0002943 
2962 
2978 
2980 
2987 

M              1.0002993 
N                       3003 
0                       3015 

P               1.0003023 

Q                  3031 

R                       3°43 

S                1-0003053 
T                       3064 

u                3075 

(b)  The  following  are  compiled  mostly  from   a  table  published  by  Briihl  (Zeits.  fur  Phys.  Chem.  vol.  7, 
pp.  25-27).     The  numbers  are  from  the  results  of  experiments  by  Biot  and  Arago,  Dulong,  Jamin,  Ketteler, 
Lorenz,  Mascart,  Chappius,  Rayleigh,  and  Riviere  and  Prytz.     When  the  number  given  rests  on  the  authority 
of  one  observer  the  name  of  that  observer  is  given.     The  values  are  for  o°  Centigrade  and  760  mm.  pressure. 

Substance. 

Kind  of 
light. 

Indices  of  refraction 
and  authority. 

Substance. 

Kind  of 
light. 

Indices  of  refraction 
and  authority. 

Acetone  . 

Ammonia 
u 

Argon  .     . 
Benzene   . 

.    . 

D 

white 
D 
D 
D 

I.OOI079-I.OOIIOO 
1.000381-1.000385 
1.000373-1.000379 
1.000281  Rayleigh. 
1.001700-1.001823 

Hydrogen     .    . 

Hydrogen  sul-  ( 
phide    .     .     I 
Methane  .    .    . 

white 
D 
D 
D 

white 

1.000138-1.000143 
1.000132  Burton. 
1.000644  Dulong. 
1.000623  Mascart. 
1.000443  Dulong. 

Bromine  .     .     . 
Carbon  dioxide 

((                           U 

Carbon  disul-    ( 
phide    .     .     { 

D 
white 
D 
white 
D 

1.001132  Mascart. 
1.000449-1.000450 
1.000448-1.000454 
1.001500  Dulong. 
1.001478-1.001485 

« 

Methyl  alcohol. 
Methyl  ether     . 

Nitric  oxide  .     . 
«          « 

D 
D 
D 

white 
D 

1.000444  Mascart. 
1.000549-1.000623 
1.000891  Mascart. 
1.000303  Dulong. 
1.000297  Mascart. 

Carbon  mon-     ( 
oxide    .     .     ( 

Chlorine  .    .     . 

n 

Chloroform  .     . 

white 
white 
white 
D 
D 

1.000340  Dulong. 
1.000335  Mascart. 
1.000772  Dulong. 
1.000773  Mascart. 
1.001436-1.001464 

Nitrogen  .    .    . 
« 

Nitrous  oxide   . 
"          " 
Oxygen    .     .    . 

white 
D 
white 
D* 
white 

1.000295-1.000300 
i  .000296-1  .000298 
1.000503-1.000507 
1.000516  Mascart 
i  .00027  2-1  .000280 

Cyanogen     .     . 

«( 

Ethyl  alcohol    . 
Ethyl  ether  .     . 
Helium    .     .     . 

white 
D 
D 
D 
D 

1.000834  Dulong. 
1.000784-1  .000825 
1.000871-1.000885 
1.001521-1.001544 
1.000036  Ramsay. 

0, 

Pentane    .    .     . 

Sulphur  dioxide 
«             « 

Water.     .    .     . 

D 
D 

white 
D 
white 

1.000271-1.000272 
1.001711  Mascart. 
1.000665  Dulong. 
1.000686  Ketteler. 
1.000261  Jamin. 

Hydrochloric     ( 
acid  ...     | 

white 
D 

1.000449  Mascart. 
1.000447        " 

« 

D 

1.000249-1.000259 

TABLES  182-1 84.-THE   REFLECTION   OF   LIGHT. 


According  to  Fresnel  the  amount  of  light  reflected  by  the  surface  of  a  transparent  medium 
=  \(A  +  B)  =  \\  ^j;~^|  +  ^j;'"^  \lA\B  the  amount  polarized  in  the  plane  of  inci- 
dence ;  B  is  that  polarized  perpendicular  to  this  ;  i  and  r  are  the  angles  of  incidence  and  refraction. 
TABLE  182. -Light  reflected  when  /     0    or  Incident  Light  Is  Normal  to  Surface. 


n. 

I  (A+B). 

n. 

I  (A  +  B). 

«. 

JM  +  -»). 

n. 

It  (A  +  B). 

I.  CO 

0.00 

1.4 

2.78 

2.0 

ii.  ii 

5- 

44.44 

I.  O2 
1.05 
I.I 

0.0  1 

0.06 
0.23 

jj 

4.00 

5-33 
6.72 

2.25 

2-5 
2-75 

14.06 

18.37 
22.89 

5-83 
10. 

IOO. 

50.00 
66.67 
96.08 

1.2 

0.83 

1.8 

8.16 

3- 

25.00 

00 

100.00 

i-3 

1.70 

1.9 

9-63 

4- 

36.00 

TABLE  183.— Light  reflected  when  n  Is  near  Unity  or  equals  1  +  dn. 


i. 

A. 

B. 

IU-H* 

A-B* 
A+B 

0° 

I.OOO 

I.OOO 

I.OOO 

0.0 

5 

1.015 

.985 

I.OOO 

1.5 

10 

1.063 

I.OOI 

6.2 

15 

1.149 

.862 

1.005 

14-3 

20 

1.282 

•752 

1.017 

26.O 

25 

1.482 

.612 

1.047 

41-5 

30 

1.778 

.444 

I.  Ill 

00.0 

35 

2.221 

.260 

1.240 

79.1 

40 

2.904 

.088 

1.496 

94-5 

45 

4-000 

.000 

2.OOO 

1  00.0 

50 

5.857 

.176 

3.016 

94.5 

9-239 

1.081 

5.160 

79.1 

60 

I6.OOO 

4.000 

10.000 

60.0 

65 

3  ^346 

12.952 

22.149 

41-5 

70 

73-079 

42.884 

57.981 

26.0 

75 

222.85 

167.16 

195.00 

14.3 

80 
85 

1099.85 
17330.64 

i68o8io8 

1035-53 
17069.36 

6.2 

90 

00 

00 

oo 

0.0 

TABLE  184.  —  Light  reflected  when  n  =  1.55. 


r> 

J  A    4. 

»T>    J. 

A-B* 

it 

r. 

A. 

/>. 

a  A  ,T 

tta»\ 

h  (A  +  B). 

A+B 

o     / 
o 

0       / 

o    o.o 

4.65 

4-65 

o  130 

0.130 

4-65 

0.0 

5 

3  13-4 

4.70 

4.6l 

131 

.129 

4-65 

I.O 

10 

6  25.9 

4.84 

4-47 

135 

.126 

4.66 

4.0 

15 

9  36.7 

5-09 

4.24 

141 

.121 

4.66 

9.1 

20 

12  44.8 

5-45 

3-92 

.15° 

.114 

4.68 

16.4 

25 

15  49-3 

5-95 

3-50 

101 

.105 

4-73 

25-9 

3° 

18  49-1 

6.64 

3-00 

175 

.094 

4.82 

37-8 

35 
40 

21  43-1 
24  30.0 

7-55 
8.  77 

2.40 

i-75 

191 
.210 

«§i 

.066 

4.98 
5-26 

5'-7 
66.7 

45 

27     8.5 

10.38 

1.08 

.233 

•049 

5-73 

81.2 

5° 

29  37-J 

12.54 

0.46 

.263 

.027 

6.50 

92.9 

55 

3i  54-2 

15-43 

0.05 

.303 

•007 

7-74 

99-3 

60 

33  58-1 

19-35 

0.12 

-342 

-.013 

9-73 

98.8 

65 

35  47-° 

24.69 

I-I3 

•375 

—.032 

12.91 

91.2 

70 

37  '9-' 

31.99 

4.00 

.400 

—.050 

18.00 

77-7 

75 

38  32.9 

42.00 

10.38 

.410 

—.060 

26.19 

61.8 

80 

39  26.8 

55-74 

23.34 

•370 

-.069 

39  54 

41.0 

82  30 

39  45-9 

64.41 

34-°4 

.320 

-.067 

49.22 

30.8 

85    o 

39  59«6 

74-52 

49-03 

.250 

—.061 

61.77 

2O.6 

86    o 

40    3-6 

79.02 

56.62 

.209 

—•055 

67.82 

16.5 

87    o 

40    6.7 

83.80 

65-32 

.163 

—.046 

74.56 

12.4 

88    o 

40    8.9 

88.88 

75-31 

.118 

—.036 

82.10 

8.3 

89    o 

40   10.2 

94.28 

86.79 

.063 

—  .022 

00.54 

4.1 

90    o 

40   10.7 

100.00 

IOO.OO 

.000 

—  .000 

100.00 

0.0 

Angle  of  total  polarization  =  57°  io'.3,  A  =  16.99. 

*  This  column  gives  the  degree  of  polarization.  t  Columns  5  and  6  furnish  a  means  of 

determining  A  and  B  for  other  values  of  «.   They  represent  the  change  in  these  quantities  for  a  change  of  «  of  0.01. 

Taken  from  E.  C.  Pickering's  "  Applications  of  Fresnel's  Formula  for  the  Reflection  of  Light." 
SMITHSONIAN  TABLES. 


192  TABLE  185. 

REFLECTION  OF  METALS. 

Perpendicular  Incidence  and  Reflection. 
The  numbers  give  the  per  cents  of  the  incident  radiation  reflected. 


p 

M 

* 

•tf 

*4 

j 

1 

o 

I 

| 

fc 

^+ 

I! 

m  Metal. 
i.ZStt. 

-Si 

j 

j 

t 

j 

,1 

B 

I 

| 

1 

1 

1 

1 

S  + 

aj    ** 

=t 

1  + 

j*^ 
.y  « 

If 

l'| 

If 

it 

1't 

il 

|q 

8 

1 

| 

SJ 

& 

m  7s 

&M 

&••« 

I 

°| 

1 

u  8 

J5-iJ 
°^ 

°l 

«  § 

w^ 

g 

^ 

ra 

« 

rt 

If 

J**        28 

i 

^k 

g 

E 

w 

B9 

1 

• 

i 

j 

o 

1 

0 

OQft 

N 

D 

* 

M 

_ 

_ 

67.0 

35-8 

29.9 

37-8 

_ 

32-9 

25-9 

33-8 

38-8 

_ 

34.1 

.288 

— 

— 

70.6 

37-1 

37-7 

42.7 

— 

35"° 

24-3 

38.8 

34-0 

— 

21.2 

.305 

*>  T  f~\ 

— 

- 

72.2 

37-2 

41.7 

44.2 

— 

37-2 

25-3 

39-8 

31.8 

- 

9.1 

.310 
.326 

_ 

_ 

75-5 

39-3 

_ 

45-2 

_ 

40-3 

24-9 

41.4 

28.6 

_ 

4-2 
I4.6 

.338 

- 

- 

- 

46.5 

- 

- 

- 

- 

- 

55-5 

•357 
•385 

- 

- 

81.2 
83.9 

43-3 
44-3 

51.0 

49.6 

- 

45-° 
47-8 

27-3 
28.6 

434 
454 

27.9 

27.1 

- 

74-5 
81.4 

.420 

_ 

_ 

83.3 

47.2 

564 

56.6 

_ 

5i-9 

3^.7 

51.8 

29-3 

_ 

86.6 

450 
.500 

857 

86.6 

72.8 
70.9 

834 
83-3 

49.2 

49-3 

60.0 
63.2 

594 
60.8 

48.8 
53-3 

544 
54-8 

37-0 
43-7 

47.0 

_ 

90-5 

•55° 

88.2 

71.2 

82.7 

48.3 

64.0 

62.6 

59-5 

54.9 

47-7 

St.  i 

74.0 

— 

92.7 

.600 
.650 

88.1 
89.1 

69.9 

83.0 
82.7 

47-5 

64-3 
654 

64.9 
66.6 

83-5 
89.0 

554 
564 

71.8 
80.0 

64.2 

66.5 

88.9 

— 

92.6 

94-7 

.700 

89.6 

72.8 

83-3 

54-9 

66.8 

68.8 

90.7 

57.6 

83-1 

69.0 

92-3 

•~ 

954 

.800 

P. 

_ 

84-3 

63-1 

_ 

69.6 

_ 

58.0 

88.6 

70.3 

94-9 

_ 

96.8 

I.O 

— 

— 

84.1 

69.8 

70-5 

72.0 

— 

63.1 

90.1 

72.9 

— 

97.0 

2.0 

__ 

~ 

aj 

£S 

75-o 
80.4 

78.6 
83.5 

~ 

70.8 
76.7 

93-8 
95-5 

B3 

97.3 
96.8 

91.0 

97*8 

3«o 

- 

- 

874 

854 

86.2 

88.7 

- 

83-0 

97.1 

88.8 

- 

93-7 

98.1 

4.0 

— 

— 

88.7 

87.1 

88.5 

91.1 

— 

87.8 

97-3 

9I-S 

96.9 

95-7 

98.5 

S-o 

- 

- 

89.0 

87.3 

89.1 

944 

- 

89.0 

97-9 

93-5 

97.0 

95-9 

98.1 

7.0 

— 

— 

90.0 

88.6 

90.1 

94-3 

— 

92.9 

98.3 

95.5 

98.3 

97.0 

98.5 

9.0 

— 

— 

90.6 

90.3 

92.2 

95-6 

— 

92.9 

984 

954 

98.0 

97-8 

98.7 

I  I.O 

- 

- 

90.7 

90.2 

92.9 

95-9 

- 

94.0 

98.4 

95-6 

98.3 

96.6 

98.8 

14.0 

92.2 

90-3 

93-6 

97.2 

96.0 

97-9 

96.4 

97-9 

98.3 

Based  upon  the  work  of  Hagen  and  Rubens,  Ann.  der  Phys.  (i)  352,  rooo;  (8)  i,  igoa;  (n)  873,  1903. 
Taken  partly  from  Landolt-Bornstein-Meyerhoffer's  Physikalisch-chemische  Tabellen. 
Further  references:  Nichols,  Wied.  Ann.  60,  401,  1897. 

Conroy,  Proc.  Roy.  Soc.  35,  26,  1883.  Nutting,  Phys.  Rev.  13,  193,  1901. 

De  la  Provastaye  and  P.  Desains,  Ann.  Chim.  Phys.  (3)          Paschen,  Ann.  der  Phys.  4,  304,  1901. 

Rayleigh,  Proc.  Roy.  Soc.  41,  274,  1886. 

Rubens,  Wied.  Ann.  37,  249,  1889. 

Trowbridge,  Wied.  Ann.  65,  595,  1898. 


30,  276,  1850. 
Langley,  Phil.  Mag.  (5)  3 
Mach  and  Schumann,  Wien.  Ber.  108,  135,  1899. 


Mag.  (5)  27,  10, 1889. 


SMITHSONIAN  TABLES* 


TABLES  186-188. 
TRANSMISSIBILITY  FOR  RADIATION  OF  JENA  GLASSES. 

TABLE  186. 

Coefficients,  a,  in  the  formula  It  =  foa*,  where  /o  is  the  Intensity  before,  and  ft  after,  transmission 
through  the  thickness  /,  expressed  in  centimetres.  Deduced  from  observations  by  Mtiller, 
Vogel,  and  Rubens  as  quoted  in  Hovestadt's  Jena  Glass  (English  translation). 


Coefficient  of  transmission,  a. 

Type  of  Glass. 

•375  M 

390ft 

•400ft 

•434ft 

•436ft 

.455M 

•477  M 

•5<>3At 

•580  M 

•677ft 

O  340,  Ord.  light  flint 
O  102,  HVy  silicate  flint 

.388 

•456 

.025 

.614 
463 

.569 
.502 

.680 
,S66 

'lit 

.880 
.700 

.880 
.782 

.878 
.828 

•939 
•794 

O   93,  Ord.         "        " 

— 

— 

.714 

.807 

•899 

.871 

•9°3 

•943 

0203,     "           "    crown 
O  598,  (Crown) 

.583 

•583 

.695 

.667 

.806 

•797 

.822 
.770 

.860 
.771 

.872 
.776 

.872 
.818 

•903 
.860 

»= 

o.7ft 

0.95ft 

i.i  ft 

1.4  ft 

i.jft. 

2.0ft 

2.3ft 

2.5ft 

a.7ft 

2.9  M 

3-i  ft 

S  204,  Borate  crown 

I.O 

.90 

•« 

•37 

.21 

.12 

.025 

.02 

.04 

•°3 

S  179,  Med.  phosp.  cr. 

— 

.82 

.61 

•37 

•17 

.Ol8 

.08 

•2S 

O  1  143,  Dense,  bor.  sil.  cr. 

- 

- 

•74 

.61 

•5° 

•33 

.18 

•034 

.06 

.021 

O  1092,  Crown 

.91 

.67 

.61 

.90 

•91 

.41 

.14 

•°33 

.006 

.07 

•043 

0451,  Light  flint 

»o2 
I.O 

_ 

.91 
.91 

.90 

.82 
.82 

il 

•33 
•45 

.10 
•17 

38 

.04 
.002 

.010 

.019 

O  469,  Heavy  " 

I.O 

- 

.82 

- 

.91 

.82 

.82 

•74 

•33 

.017 

.010 

O  500,        "       " 

I.O 

— 

I.O 

— 

I.O 

— 

I.O 

.90 

•45 

.050 

.019 

S  163,        «      « 

I.O 

.82 

.91 

.91 

•55 

**3 

.062 

TABLE  187. 

Note :  With  the  following  data,  /  must  be  expressed  in  millimetres ;  i.  e.  the  figures  as  given 
give  the  transmissions  for  thickness  of  I  mm. 


No.  and  Type  of  Glass. 

Wave-length  in  ft. 

Visible  Spectrum. 

Ultra-violet  Spectrum. 

.644ft 

•578ft 

•546/4 

.509  ft 

.480  ft 

•436ft 

•405ft 

•384M 

.361  ft 

•340ft 

•332ft 

•309ft 

.aSa-ft 

F38i5  Dark  neutral 

•35 

•3S 

•37 

•35 

•34 

•30 

•15 

.06 

F45I2  Red  filter 

.94 

.os 

F2745  Copper  ruby 
F43I3  Dark  yellow 
F435I  Yellow 

.72 
.98 
.98 

•39 
•97 
•97 

•47 

$ 

% 

•93 

45 
.09 

•44 

•43 
•IS 

•43 

F4937  Bright  yellow 

I.O 

1.0 

I.O 

•99 

•74 

.40 

•31 

.28 

.22 

,18 

.14 

.06 

F  4930  Green  filter 

•17 

•So 

.64 

.62 

•44 

F3873  Blue  filter 

— 

.18 

•SO 

•73 

•69 

•S9 

.36 

.10 

F  3654     Cobalt    glass, 

transparent  for  outer 

red 

— 

— 

— 

•IS 

•44 

•8S 

I.O 

I.O 

I.O 

I.O 

1.0 

•S8 

F  3653  Blue,  ultraviolet 
F  3728  Didymium,str'g 
bands 

.99 

.72 

•99 

.96 

.11 

•95 

.65 
.96 

I.O 

•99 

I.O 

•99 

I.O 

.89 

1.0 

.89 

I.O 

•77 

.81 

•54 

.18 

This  and  the  following  table  are  taken  from  Jenaer  Glas  fur  die  Optik,  Liste  751,  1909, 
TABLE  188.  -  Transmf  ssibility  of  Jena  Ultra-violet  Glasses. 


No.  and  Type  of  Glass. 

Thickness. 

0.397  ft 

0.383  ft 

0.361  ft 

0.346  M. 

0.325  ft 

0,0,  „ 

0.280  ft 

UV  3199  Ultra-violet 

i  mm. 
2  mm. 

1.00 

0.99 

I.OO 

0.99 

I.OO 

0.99 

I.OO 

0.97 

I.OO 

0.90 

0.95 
0.57 

0.56 

M                            « 

i  dm. 

o-95 

0.95 

0.89 

0.70 

0.36 

UV  3248        " 

I  mm. 

I.OO 

I.OO 

I.OO 

I.OO 

0.98 

0.91 

0.35 

"                " 

2  mm. 

0.98 

0.98 

0.98 

0.92 

0.78 

0.38 

i  dm. 

0.96 

0.87 

0.79 

0.45 

0.08 

SMITHSONIAN  TABLES. 


TABLE    189. 
TRANSMISSIBILITY    FOR    RADIATION. 

Transmissibility  of  the  Various  Substance!  of  Tables  166  to  175. 

Alum  :  Ordinary  alum  (crystal)  absorbs  the  infra-red. 

Metallic  reflection  at  9.05/4  and  30  to  40/4. 

Rock-salt :  Rubens  and  Trowbridge  (Wied.  Ann.  65,  1898)  give  the  following  transparencies  for 
a  i  cm.  thick  plate  in  % : 


X 

9 

10 

12 

13 

H 

15 

16 

17 

18 

19 

20.7 

23-7A* 

99-5 

99-5 

99-3 

97.6 

93-i 

84.6 

66.1 

51.6 

27-5 

9.6 

0.6 

0. 

Pfliiger  (Phys.  Zt.  5.  1904)  gives  the  following  for  the  ultra-violet,  same  thickness  :  280/1/1,  95.5% ; 

231,86%;  210,77%;  186,  70%. 
Metallic  reflection  at  0.110/4,  0.156,  51.2,  and  87/1. 
Sylvinc :  Transparency  of  a  i  cm.  thick  plate  (Trowbridge,  Wied.  Ann.  60,  1897). 


X 

% 

9 

10 

II 

12 

U 

H 

15 

16 

17 

18 

19 

20.7 

23-7/* 

100. 

98.8 

99.0 

99-5 

99-5 

97-5 

95-4 

93-6 

92. 

86. 

76. 

58. 

15- 

Metallic  reflection  at  o.i 
Fluorite  :  Very  transpare 
Rubens  and  Trowbridge 

114/4,  0.161,  61.1,  loo. 
nt  for  the  ultra-violet  nearly  to  0.1/4. 
give  the  following  for  a  i  cm.  plate  (Wied.  Ann.  60,  1897)  : 

X 

8/4 

9 

10 

ii 

12/4 

% 

84.4 

54-3 

16.4 

I.O 

0 

Metallic  reflection  at  24/4,  31.6,  40/1. 

Iceland  Spar :   Merritt  (Wied.  Ann.  55,  1895)  Sives  the  following  values  of  k  in  the  formula 
i=i0e-kd  (d  in  cm.): 
For  the  ordinary  ray : 


X 

1.  02 

1-45 

1.72 

2.07 

2.II 

2.30 

2.44 

2-53 

2.60 

2.6S 

2.74/4 

k 

0.0 

o.o 

0.03 

0.13 

0.74 

1.92 

3.00 

1.92 

I.2I 

1.74 

2.36 

X 

2.83 

2.90 

2.95 

3.04 

3-30 

3-47 

3-62 

3-8o 

3-98 

4-35 

4.52 

4.83A* 

k 

1.32 

0.70 

1.80 

4.71 

22.7 

19.4 

9.6 

18.6 

00 

6.6 

14-3 

6.1 

For  the  extraordinary  ray  : 


X 

2.49 

2.87 

3.00 

3-28 

3.38 

3-59 

376 

3-90 

4.02 

4.41 

4.67/4 

k 

0.14 

0.08 

0-43 

1.32 

0.89 

1.79 

2.04 

1.17 

0.89 

1.07 

2.40 

X 

4.91 

5-04 

5-34 

5-5°A* 

k 

1.25 

2.13 

4.41 

12.8 

Quartz:  Very  transparent  to  the  ultra-violet;  Pfliiger  gets  the  following  transmission  values  for 

a  plate  i  cm.  thick:  at  0.222/4,  94.2%;  0.214,  92  ;  0.203,  83-6;  0.186,  67.2%. 
Merritt  {Wied.  Ann.  55,  1895)  gives  the  following  values  for  k  (see  formula  under  Iceland  Spar) : 
For  the  ordinary  ray : 


X 

2.72 

2.83 

2-95 

3-07 

3-17 

3-38 

3-67 

3-82 

3.96 

4.12 

4-50A* 

k 

O.2O 

0-47 

0-57 

0.31 

0.20 

0.15 

1.26 

1.61 

2.04 

3-41 

7-30 

For  the  extraordinary  ray  : 


X 

2.74 

2.89 

3.00 

3.08 

3-26 

3-43 

3-52 

3-59 

3-64 

3-74 

3-9i 

4.19 

4.36ju 

k 

o.o 

O.I  I 

0-33 

0.26 

O.I  I 

0.51 

0.76 

1.88 

1.83 

1.62 

2.22 

3-35 

8.0 

For  \>7  f^  becomes  opaque,  metallic  reflection  at  8.50/4,  9.02,  20.75-24.4/4,  then  trans- 
parent again. 

The  above  are  taken  from  Kayser'i "  Handbuch  der  Spectroscopie,"  vol.  iii. 
SMITHSONIAN  TABLES. 


TABLES  190-191. 
TRANSMISSIBILITY  FOR  RADIATION. 

TABLE  190.  — Color  Screens. 


195 


The  following  light-filters  are  quoted  from  Landolt's  "  Das  optische  Drehungsvermogen,  etc."  1898. 
Although  only  the  potassium  salt  does  not  keep  well  it  is  perhaps  safer  to  use  freshly  prepared 
solutions. 


Thick- 

Grammes of 

Optical  cen- 

Color. 

ness. 

Water  solutions  of 

substance 

tre  of  band. 

Transmission  . 

mm. 

in  100  c.cm. 

M 

Red 

« 

20 
20 

Crystal-violet,  56  O 
Potassium  monochromate 

0.005 
IO. 

0.6659 

j  begins  about  0.718/14. 
(  ends  sharp  at  0.639/4. 

Yellow 

20 

Nickel-sulphate,  NiSO^aq. 

30- 

0.5919 

0.614-0.574/4, 

« 

IS 

Potassium  monochromate 

10. 

M 

Green 

IS 
20 

Potassium  permanganate 
Copper  chloride,  CuCla.2aq. 

0.025 
60. 

0-5330 

0.540-0.  505/4 

«« 

Bright  ( 
blue  } 
Dark 

20 
20 
20 
20 

Potassium  monochromate 
Double-green,  SF 
Copper-sulphate,  CuSO^aq. 
Crystal-violet,  560 

IO. 
0.02 

IS- 
0.005 

0.4885 
0.4482 

j  0.526-0.494  and 
|  0.494-0.458/4 

0.478-0.410/4 

blue  1 

20 

Copper  sulphate,  CuSO^aq. 

IS- 

TABLE  191. -Color  Screens. 

The  following  list  is  condensed  from  Wood's  Physical  Optics,  2nd  edition : 

Methyl  violet,  48.-  (Berlin  Anilin  Fabrik)  very  dilute,  and  nitroso-dimethyl-anilme  transmits  0.365/4. 

Methyl  violet  -f-  chinin-sulphate  (separate  solutions),  the  violet  solution  made  strong  enough  to 

blot  out  0.4359/4,  transmits  0.4047  and  0.4048,  also  faintly  0.3984. 
Cobalt  glass  -f-  aesculin  solution  transmits  0.4359/4. 
Guinea  green  B  extra  (Berlin)  -j-  chinin  sulphate  transmits  0.4916/4. 
Neptune  green  (Bayer,  Elberfeld)  +  chrysoidine.     Dilute  the  latter  enough  to  just  transmit  0.5790 

and  0.5461 ;  then  add  the  Neptune  green  until  the  yellow  lines  disappear. 
Chrysoidine  -f-  cosine  transmits  0.5790/4.     The  former  should  be  dilute  and  the  cosine  added  until 

the  green  line  disappears. 
Silver  chemically  deposited  on  a  quartz  plate  is  practically  opaque  except  to  the  ultra-violet  region 

0.3160-0.3260  where  90%  of  the  energy  passes  through.     The  film  should  be  of  such  thickness 

that  a  window  backed  by  a  brilliantly  lighted  sky  is  barely  visible. 
In  the  following  those  marked  with  a  *  are  transparent  to  a  more  or  less  degree  to  the  ultra-violet: 

*  Cobalt  chloride:  solution  in  water,  —  absorbs  O.5O-.53/4;  addition  of  CaCl2  widens  the  band  to 
0.47-. 50.     It  is  exceedingly  transparent  to  the  ultra-violet  down  to  0.20.     If  dissolved  in  methyl 
alcohol  -f  water,  absorbs  O-5O-.53  and  everything  below  0.35.     In  methyl  alcohol  alone  0.485- 
0.555  and  below  0.40/4. 

Copper  chloride :  in  ethyl  alcohol  absorbs  above  0.585  and  below  0.535  '>  m  alcohol  +  50%  water, 

above  0.595  and  below  0.37/4. 
Neodymium  salts  are  useful  combined  with  other  media,  sharpening  the  edges  of  the  absorption 

bands.  In  solution  with  bichromate  of  potash,  transmits  0.535-. 565  and  above  0.60/4,  the  bands 

very  sharp  (a  useful  screen  for  photographing  with  a  visually  corrected  objective). 
Praesodymium  salts :  three  strong  bands  at  0.482,  .468,  .444.    In  strong  solutions  they  fuse  into  a 

sharp  band  at  O.435-.485/4.     Absorption  below  0.34. 
Picric  acid  absorbs  o.  36-42/4,  depending  on  the  concentration. 
Potassium  chromate  absorbs  O.4O-.35,  O-3O-.24,  transmits  0.23/4. 

*  Potassium  permanganate:  absorbs 0.5 5 5-. 50,  transmits  all  the  ultra-violet. 

Chromium  chloride  :  absorbs  above  0.57,  between  0.50  and  .39,  and  below  0.33/4.    These  limits 

vary  with  the  concentration. 
Aesculin  :  absorbs  below  0.363/4,  very  useful  for  removing  the  ultra-violet. 

*  Nitroso-dimethyl-aniline :  very  dilute  aqueous  solution  absorbs  O.49-.37  and  transmits  all  the 
ultra-violet. 

Very  dense  cobalt  glass  -f-  dense  ruby  glass  or  a  strong  potassium  bichromate  solution  cuts  off 

everything  below  0.70  and  transmits  freely  the  red. 
Iodine :  saturated  solution  in  CS2  is  opaque  to  the  visible  and  transparent  to  the  infra-red. 

SMITHSONIAN  TABLES. 


196 


TABLE  1 92. 
TRANSMISSIBILITY  FOR  RADIATION, 

Color  Screens.    Jena  Glasses. 


Kind  of  Glass. 

Maker's 

No. 

Color. 

Region  Transmitted. 

Thick- 
ness, 
mm. 

I 

Copper-ruby  . 

2728 

Deep  red      .... 

Only  red  to  o.6jt  

1.7 

la 

Gold-ruby  .    .    . 

4  CO™ 

Red     

j  Red,  yellow  ;  in  thin  layers  also 

2 

2a 
3 

Uranium    .    .    . 
« 

Nickel    .... 
Chromium      •    . 

454ra 
455m 

440** 
4i4UI 

Bright  yellow  .    .    . 

I  Bright  yellow,  fluo- 
}      resces. 

Bright  yellow-brown 
Yellow-green    .    . 

(      blue  and  violet. 
(  Red,  yellow,  green  to  Et  ;   in  ) 
(      thin  layer  also  blue                J 

(  Red,  yellow,  green  (weakened),  ) 
(      blue  (very  weakened)             ) 
Yellowish-green    

16. 

II. 

IO. 

4a 

A.b 

« 
Green  copper  . 

«2 

41Iin 

Greenish-yellow   .     . 
Green  ...         .     . 

Red,  green;  from  0.65-.  50/1*   .     .     . 
Green  yellow  some  red  and  blue 

5- 

2—  •? 

1 

Chromium  .     .     . 
Copper  chromium 

&- 
476111 

Yellow-green   .     .    . 
Grass-green 

Yellowish-green,  some  red    .    .     . 
Green      

•  J 
2-5 

Green-filter     .    . 
«        « 

§c 

Dark  green  .... 

u             « 

Green  (in  thin  sheets  some  blue)   . 

5- 

10 

Copper            . 

2742 

Blue,  as  CuSC»4    .    . 

Green  blue  violet    ...... 

c_i2 

1  1 

Blue-violet     . 

447in 

Blue,  as  cobalt  glass 

Blue  violet  

M 

12 

««       «i 
Cobalt  .     .    .    . 

M 

A2AUI 

«     «      «          « 
Blue    

(  Blue,  violet,  blue-green  (weak-  ) 
(      ened),  no  red                            J 
Blue  violet  extreme  red       .    . 

• 

2-5 

4_r 

13 
H 
I  c 

Nickel    .... 
Violet    .... 
Gray       .... 

45°IU 

452"! 

444IU 

Dark  violet  .... 
«        « 

)  Grav.  no  recosr-  ) 

Violet  (G-H),  extreme  red    ... 
Violet  (G-H),  some  weakened  .     . 

V 

o  1-8 

16 

i< 

44*™ 

f     nizable  color     \ 

All  parts  of  the  spectrum  weakened 

O  I—"? 

<*<+:> 

<_>.!       J 

See  "  Uber  Farbgl'aser  fur  wissenschaftliche  und  technische  Zwecke,"  by  Zsigmondy,  Z.  fur  In- 
strumentenkunde,  21,  1901  (from  which  the  above  table  is  taken),  and  "  Cber  Jenenser  Licht- 
filter,"  by  Grebe,  same  volume. 
(The  following  notes  are  quoted  from  Everett's  translation  of  the  above  in  the  English  edition  of 

Hovestadt's  "  Jena  Glass.") 
Division  of  the  spectrum  into  complementary  colors : 

1st  by  2728  (deep  red)  and  2742  (blue,  like  copper  sulphate). 
2nd  by  454™  (bright  yellow)  and  447'"  (blue,  like  cobalt  glass). 
3rd  by  433™  (greenish-yellow)  and  424m  (blue). 
Thicknesses  necessary  in  above  :  2728,  1.6-1.7  mm. ;  2742,5;  4S4ra,  16;  447™,  1.5-2.0;  433™, 

2.5-3.5;  424m,  3mm. 

Three-fold  division  into  red,  green  and  blue  (with  violet) : 
2728,  1.7  mm. ;  4i4m,  10  mm.;  447111,  1.5  mm.,  or  by 
2728,  1.7  mm. ;  436111,  2.6mm. ;  447™,  1.8  mm. 

Grebe  found  the  three  following  glasses  specially  suited  for  the  additive  methods  of  three-color 
projection : 

2745,  red;  438m,  green;  447m,  blue  violet; 

corresponding  closely  to  Young's  three  elementary  color  sensations. 
Most  of  the  Jena  glasses  can  be  supplied  to  order,  but  the  absorption  bands  vary  somewhat  in 

different  meltings. 

See  also  "  Atlas  of  Absorption  Spectra,"  Uhler  and  Wood,  Carnegie  Institution  Publications, 
1907. 

SMITHSONIAN  TABLES. 


TABLES  193,  194.    ROTATION  OF  PLANE  OF  POLARIZED  LIGHT.    197 

TABLE  193.  —  Tartaric  Acid;  Camphor;  Santonin;  Santonic  Acid;  Cane  Sugar. 

A  few  examples  are  here  given  showing  the  effect  of  wave-length  on  the  rotation  of  the  plane  of  polarization.  The 
rotations  are  for  a  thickness  of  one  decimetre  of  the  solution.  The  examples  are  quoted  from  Landolt  &  Born- 
stem's  "  Phys.  Chem.  Tab."  The  following  symbols  are  used  :  — 

/  =  number  grammes  of  the  active  substance  in  100  grammes  of  the  solution. 

c  =  solvent        " 

q  =  active         "  "    cubic  centimetre     " 

Right-handed  rotation  is  marked  +,  left-handed  — . 


Line  of 

Wave-length 
according  to 

Tartaric  acid,*  CuH6O6, 
dissolved  in  water. 

Camphor,*  C10H16O, 
dissolved  in  alcohol. 

Santonin,t  C16H18Os, 
dissolved  in  chloroform. 

spectrum. 

Angstrom  in 
cms.  X  io6. 

?  —  5°  to  95> 
temp.  =  24°  C. 

q  =  50  to  95, 
temp.  =  22.9°  C. 

9=  75  to  96.5, 
temp.  =  20°  C. 

B 
C 
D 
E 

68.67 
65.62 
58.92 
52.69 

+  20.748  +  0.09446? 

+  1.950  +  0.13030? 
+  0.153  +  0.17514? 

38°.  549  —  0.0852? 

51.945  —  0.0964? 
74.331—0.1343? 

—  140°.!     +0.2085? 
—  149.3    +0.1555? 
—  202.7    +0.3086? 
—  285.6    +  0.5820  ? 

bi 

b2 

5I-83 

—  0.832  +  0.19147? 

79.348  —  0.1451? 

—  302.38  +  0.6557  ? 

F 

e 

48.61 
43-83 

—  3-598  +  0.23977? 
—  9.657  +  0.31437? 

99.601  —  0.1912  ? 
149.696  —  0.2346  q 

—  365.55  +  0.8284  ? 
534-98+I.5240? 

Santonin.t  C15H18O3, 

Santonic  acid,t 

Santonin  ,t  C1RH18O3,  * 
dissolved  in  alcohol. 
c  —  1.782 

dissolved  in 
alcohol. 

dissolved  in 
chloroform 

dissolved  in 
chloroform. 

dissolved  in 

temp.  =  20°  C. 

c  =4.046. 
temp.  = 

20°  C. 

c=  3-  i-3o.  5. 
temp.  = 

20°  C. 

£•  =  27.192. 
temp.  =  20°  C. 

P  —  io  to  30. 

B 

68.67 

—  110.4° 

442° 

484° 

-49° 

47°-56 

C 
D 

65.62 
58.92 

—  II8.8 

—  161.0 

5°4 
693 

549 

—  57 
—  74 

52-70 
60.41  - 

E 

52.69 

222.6 

991 

1088 

—  105 

84-56 

bi 

5I-83 

—  237.1 

1148 

—  112 

bg 

— 

— 

— 

— 

87.88 

F 

48.61 

261.7 

*323 

1444 

—  137 

101.18 

e 

43-83 

—  380.0 

201  1 

22OI 

—  197 

_ 

G 

43-°7 

— 

— 

— 

131.96 

g 

42.26 

— 

2381 

26lO 

—  230 

*  Arndtsen,  "  Ann.  Chim.  Phys."  (3)  54,  1858. 
t  Narini,  "  R.  Ace.  dei  Lincei,"  (3)  13,  1882. 

t  Stefan,  "  Sitzb.  d.  Wien.  Akad."  52,  1865. 

TABLE  194. -Sodium  Chlorate;  Quartz. 


Sodium  chlorate  (Guye,  C.  R.  108,  1889). 

Quartz  (Soret  &  Sarasin,  Arch,  de  Gen.  1882,  or  C.  R.  95,  1882).* 

Spec- 
trum 
line. 

Wave- 
length. 

Temp. 

Rotation 
per  mm. 

Spec- 
trum 
line. 

Wave- 
length. 

Rotation 
per  mm. 

Spec- 
trum 
line. 

Wave- 
length. 

Rotation 
per  mm. 

a 

71.769 

I5°.0 

2°.068 

A 

76.04 

i2°.668 

Cd9 

36.090 

63°.628 

B 
C 
D 

67.889 
65-073 
59-085 

17.4 
2O.6 

18.3 

2.318 

2-599 

3.104 

a 
B 

71.836 
68.671 

14.304 
I5-746 

N 
Cd10 

o 

35-8I8 

34-655 
34406 

64.459 
69454 
70.587 

E 
F 

53-233 
48.912 

1  6.0 
11.9 

3.841 
4-587 

C 

65.621 
58-951 

17.318 
21.684 

Cdu 

34.015 

72.448 

G 

45-532 

IO.I 

5-331 

Da 

58.891 

21.727 

P 

33.600 

74.571 

G 

42.834 

14.5 

6.005 

V 

32.858 

78.579 

H 

40.714 

13-3 

6.754 

E 

52.691 

27.543 

Cdi2 

32470 

80.459 

L 

38.412 

14.0 

7-654 

F 

48.607 

32.773 

M 

37-352 

10.7 

8.100 

G 

43.072 

42.604 

R 

3I-798 

84.972 

N 

35-8l8 

12.9 

8.861 

Cd17 

27.467 

121.052 

P 

33-93  i 

I2.I 

9.801 

h 

41.012 

4748i 

Cd18 

25-7I3 

143.266 

Q 

32-341 

II.9 

10.787 

H 

39.68l 

3^93 

Cd28 

23.125 

190.426 

R 

30-645 

11.921 

K 

39-333 

52.155 

T 

29.918 

12.8 

12.424 

Cd24 

22.645 

201.824 

Cd17 

28.270 

12.2 

13.426 

L 

38.196 

55-625 

Cd25 

21-935 

220.731 

25.038 

II.6 

14.965 

M 

37-262 

58-894 

Cd26 

21.431 

235-972 

*  The  paper  is  quoted  from  a  paper  by  Ketteler  in  "  Wied.  Ann."  vol.  21,  p.  444.    The  wave-lengths  are  for 
the  Fraunhofer  lines,  Angstrom's  values  for  the  ultra  violet  sun,  and  Cornu's  values  for  the  cadmium  lines. 


198 


TABLE  195. 
NEWTON'S  RINGS. 

Newton's  Table  of  Colors. 


The  following  table  gives  the  thickness  in  millionths  of  an  inch,  according  to  Newton,  of  a  plate  of  air,  water,  and 
glass  corresponding  to  the  different  colors  in  successive  rings  commonly  called  colors  of  the  first,  second,  third, 
etc.,  orders. 


Color  for  re- 
flected light. 

Color  for 
transmitted 
light. 

Thickness  in 

Color 
for  trans- 
mitted 
light. 

Thickness  in 

millionths  of  an 

millionths  of  an 

1 

o 

inch  for  — 

1 
0 

Color  for  re- 
flected light. 

inch  for  — 

1 

1 

si 

1 

< 

£ 

0 

3 

ft 

3 

I. 

Very  black 

_ 

0-5 

0.4 

0.2 

Yellow.    . 

Bluish 

Black    . 

. 

White  .    . 

1.0 

0.75 

0-9 

green 

27.1 

20.3 

T7-S 

Beginning 

Red  .     .    . 

— 

29.0 

21.7 

18.7 

of  black  . 

— 

2.O 

I  r 

I>3 

Bluish  red 

— 

32.0 

24.0 

20.7 

Blue      . 

, 

Yellowish 

red.    . 

2.4 

1.8 

j   r 

IV. 

Bluish 

White  . 

, 

Black  .     . 

5-2 

3-9 

34 

green    . 

— 

24.0 

2c. 

22.0 

Yellow  . 
Orange 

• 

Violet      . 

8.0 

g 

4-6 
4.2 

Green   .    . 
Yellowish 

Red    . 

35-3 

26. 

5 

22.7 

Red.    . 

. 

Blue    .    . 

9.0 

6.7 

5.8 

green     . 

— 

36.0 

27.0 

23.2 

Red  .    .    . 

Bluish 

II. 

Violet  . 

. 

White     . 

II.  2 

34 

7-2 

green 

40-3 

30.2 

26.0 

Indigo  . 

. 

— 

12.8 

9.6 

8.4 

Blue      . 

. 

Yellow    . 

14.0 

10.5 

9.0 

V. 

Greenish 

Green   . 
Yellow  . 

; 

Red     .    . 
Violet      . 

% 

"•3 

12.2 

9-7 
10.4 

blue  .    . 
Red.    .    . 

Red   . 

46.0 
52-5 

34-5 
394 

39-7 
34-o 

Orange 

— 

17.2 

13.0 

"•3 

Bright  red 

Blue    .    . 

18.2 

137 

1  1.8 

VI. 

Greenish 

Scarlet  . 

. 

— 

19.7 

147 

12.7 

blue  .    . 

— 

58.7 

46 

38.0 

Red.    .    . 

— 

65.0 

48.7 

42.0 

III. 

Purple  . 

, 

Green 

2I.O 

'5-7 

T3-5 

Indigo  . 

( 

— 

21.  1 

17.6 

14.2 

VII. 

Greenish 

Blue      . 
Green   . 

Yellow    . 
Red     .    . 

23.2 
25.2 

'7-5 
18.6 

16.2 

blue  .     . 
Reddish 

— 

72.0 

53-2 

45-8 

white 

— 

71.0 

57- 

7 

494 

The  above  table  has  been  several  times  revised  both  as  to  the  colors  and  the  numerical 

values.     Professors  Reinold  and  Rucker,  in  their  investigations  on  the  measurement 

of  the 

thickness  of  soap  films,  found  it  necessary  to  make  new  determinations.   They  give  a  shorter 
series  of  colors,  as  they  found  difficulty  in  distinguishing  slight  differences  of  shade,  but 
divide  each  color  into  ten  parts  and  tabulate  the  variation  of  thickness  in  terms  of  the  tenth 

of  a  color  band.     The  position  in  the  band  at  which  the  thickness  is 

given  and  the  order  of 

color  are  indicated  by  numerical  subscripts.   For  example  :  RI  5  indicates  the  red  of  the  first 
order  and  the  fifth  tenth  from  the  edge  furthest  from  the  red  edge  of  the  spectrum.    The 

thicknesses  are  in  millionths  of  a  centimetre. 

J 

Color. 

Posi- 
tion. 

Thick- 
ness. 

1 

O 

Color. 

Posi- 
tion. 

Thick- 
ness. 

1 

o 

Color. 

Posi- 
tion. 

Thick- 
ness. 

I. 

Red*    . 

RIB 

28.4 

Red*    . 

R3  5 

76.5 

VI. 

Green    . 

Ge  o 

141.0 

Bluish 

Green* 

G65 

147.9 

II. 

Violet   . 

V26 

30.5 

red  *  .    ] 

BR36 

8l.5 

Red  .     . 

R6o 

154.8 

Blue  .    . 

B26 

35-3 

Red*    . 

Res 

162.7 

Green    . 

G26 

40.9 

IV. 

Green    . 

G4  o 

84.I 

Yellow  * 

Y26 

454 

H 

G46 

89.3 

VII. 

Green    . 

G70 

170.5 

Orange  * 

026 

49.1 

Yellow  ' 

Green*. 

G76 

178.7 

Red  .     . 

R2  6 

52.2 

green  *    ^ 

^G45 

96.4 

Red  .     . 

R7o 

186.9 

Red*    . 

R46 

105.2 

Red*    . 

R?  6 

193.6 

III. 

Purple  . 

P35 

55-9 

Blue  .     . 

B3  o 

57-7 

V. 

Green    . 

GS  o 

III-9 

VIII. 

Green    . 

Gg  o 

200.4 

Blue*    . 

B35 

60.3 

Green  *  . 

G55 

II8.8 

Red  .    . 

R8o 

211.5 

Green    . 

G86 

65.6 

Red  .     . 

RS  o 

126.0 

Yellow* 

Y36 

71.0 

Red*     . 

RS  5 

J33-5 

*  The  colors  marked  are  the  same  as  the  corresponding  colors  in  Newton's  table. 
SMITHSONIAN  TABLES. 


TABLE  196. 
CONDUCTIVITY  FOR  HEAT. 


199 


The  coefficient  k  is  the  quantity  of  heat  in  small  calories  which  is  transmitted  per  second  through 
a  plate  one  centimetre  thick  per  square  centimetre  of  its  surface  when  the  difference  of  tempera- 
ture between  the  two  faces  of  the  plate  is  one  degree  Centigrade.  The  coefficient  k  is  found  to 
vary  with  the  absolute  temperature  of  the  plate,  and  is  expressed  approximately  by  the  equation 
kt  =  k0  (i  +  «*)•  In  the  table  k0  is  the  value  of  kt  for  o°  C.,  t  the  temperature  Centigrade,  and  a 
a  constant. 


Substance. 

t 

kt 

a 

t 

Substance. 

t 

kt 

1 

Aluminum    .    .  < 

o 

IOO 

0-3435  I 

.0005356 

! 

Carborundum      .    . 
Slate        .         .    . 

- 

00050 

0036 

12 
j  j 

( 

Antimony     .    .  < 

o 

IOO 

•0442  i 
.0396  J 

—  .OOIO4I 

I 

Soil  dry  

- 

00033 
0016 

II 
II 

"     wet  .... 

Bismuth   .    .    A 

o 

IOO 

.0177  ) 
.0164  ) 

—.000735 

I 

Diatomic  earth     .    . 
Fire-brick    .... 

: 

00013 
00028 

12 
12 

Brass  (yellow)   .  < 

o 

IOO 

.2041  / 
.2540  ( 

.002445 

I 

Granite    .    .   j*f 

: 

.00510 

.00550 

\6 

"      (red)    .    .j 
Cadmium      .    .  < 

0 
IOO 

o 

IOO 

.2460  1 
.2827  f 
.2200  |^ 
.2045  \ 

.001492 
—  .000705 

I 
I 

- 

.00029 
.00016 

00045 

12 
12 

Magnesia    .    j  £r°™ 
Marbles,  lime- 

Constantin          j 
6oCu-f  4oNi  .  j 

Copper     .    .     .  j 

18 

IOO 
0 
IOO 

.5402 
.6405 
•7189? 
.7226  f 

.OOOO5I 

2 

2 

stone,     cal-     ,    v 
cite,      com-^frfom 
pact     dolo- 
mite     .     . 

- 

00470 
.00560 

I6 

German  silver   .  < 

o 

IOO 

.0700  ( 
.0887  { 

.002670 

I 

Micaceous  flagstone  : 
along  cleavage  .     . 

_ 

.00632 

6 

Iron      .    .    .    .  j 

0 

IOO 

.1665) 
.1627  ( 

—  .OO0228 

I 

across  cleavage 

— 

.00441 

.00014 

6 
8 

"     (wrought)*  j 

o 

IOO 

.2070 
•1567 

- 

3 

Paraffine.     .     .    .     ) 

0 
IOO 

.00023 

.00168 

9 

Lead    .    .    .    .j 

0 

IOO 

.0836 
.0764 

—.000861 

i 

Pasteboard  .... 
Plaster  of  Paris    .     . 

— 

.00045 
.00070 

ii 

Mercury    .    .    .  < 

0 

.0148  ) 

_ 

4 

"       "    "  powder 
Quartz     .         ... 

- 

.0026 

/•WklA 

ii 

12 

Magnesium    .     . 
Manganin 
84Cu-f4Ni+( 
i2Mn     .     .     .  ( 

O-IOO 

18 

IOO 

.3760 

.5186 
.6310 

.000000 

i 

2 
2 

Sand  (white  dry)  .     . 
Sandstone  and  (  (    r 
hard  grit    frt°om 
(dry)     .    .    I    to 

- 

.00093 

.00545 
.00565 

6 
6 

Nickel  .... 

18 

.1420 

2 

Sawdust       .     . 

.00012 

8 

Palladium     .     . 

18 

.1683 

_ 

2 

Serpentine        (Corn- 

Platinum .     .     .  < 

18 

.1664 

- 

2 

wall  red)  .... 

- 

.00441 

6 

IOO 

-J733 

— 

2 

Slate  : 

Steel  (hard)  .     . 

- 

.0620 

- 

5 

along  cleav-  (  from 

- 

.00550 

6 

«      (soft)    .    . 

— 

.IIIO 

— 

5 

age    .     .    I     to 

- 

.00650 

u 

Silver  .... 

o 

1.0960 

_ 

4 

across  cleav-  (  from 

_ 

.00315 

Tin  . 

o 

IOO 

0.1528  j. 
•1423  \ 

-.000.687 

i 

age    .     .    j     to 
Snow,  compact  layers 

— 

.00360 
.00051 

7 

j 

Wood's  alloy    . 

— 

.0319 

— 

4 

Strawboard      .    .    . 

— 

.00033 

8 

Zinc      .... 

18 

-2653 

— 

2 

Vulcanite     .... 

— 

.00087 

10 

Vulcanized       j  from 

_ 

.00034 

6 

rubber  (soft)  (     to 

- 

.00054 

6 

Wax  (bees)  .... 

— 

.00009 

8 

Wood,  fir: 

parallel  to  axis  .    . 

_ 

.00030 

8 

perpendicular      to 

_ 

.00009 

8 

I  Lorenz.          4  H.  F.  Weber.         6  H.  L.  &  D.J          8  G.  Forbes.          10  Stefan. 

2  J  +  Df.        5  Kohlrausch.            7  Hjeltstrom.           9  R.  Weber.           ii  Lees-Chorlton. 
3  J.  Forbes.                                                                                                          12  Hutton-Blard. 

*  A  repetition  of  Forbes's  experiments  by  Mitchell,  under  the  direction  of  Tait,  shows  the  conductivity  to  increase 
with  rise  of  temperature.     (Trans.  R.  S.  E.  vol.  33,  1887.) 

:hel,  Let 


ipera 
t  Jaeger  and  Diesselhorst. 

SMITHSONIAN  TABLES. 


Herschel,  Lebour,  and  Dunn  (British  Association  Committee). 


2OO  TABLES  197-200. 

CONDUCTIVITY  FOR    HEAT. 

TABLE  197.  — Various  Substances.  TABLE  198.  — Water  and  Salt  Solutions. 


Au- 

Substance. 

* 

thor- 

o 

ity. 

Asbestos  paper     . 

_ 

.00043 

5 

Blotting  paper  .    . 
Carbon    .... 

o 

.00015 
.000405 

5 

I 

Portland  cement  . 

- 

.00071 

5 

Cork   .... 

o 

OOO7I7 

i 

Cotton  wool     .     . 
Cotton  pressed 

0 

.000043 
.000033 

i 

Chalk  

__ 

OO2OOO 

2 

Ebonite   .... 

49 

.OOO37O 

2 

Felt     .     . 

o 

000087 

_ 

Flannel  (dry)    .     . 

0 

.00012 

I 

i  from 

_ 

.OOI  I        ) 

(to     ... 

_ 

.0023       ) 

3 

.000087 

. 

Haircloth     .     .     . 

- 

.OOOO42 

i 

Ice       ....    | 

: 

.00223 
.00568 

i 
4 

Leather,  cow-hide 

_ 

.OOO42 

5 

"        chamois  . 

- 

.OOOI5 

5 

_ 

.OOO2I 

Silk     

_ 

.000095 

5 

Caen  stone  (build-) 
ing  limestone)   J 

- 

•00433 

2 

Gale's  sandstone  ) 
(freestone)     .    J 

- 

.00211 

2 

i  G.  Forbes.            4  Neumann. 

2  H.,  L.,  &  D.*       5  Lees-Chorlton. 

3  Various. 

Au- 

Substance. 

Density. 

* 

thor- 

ity. 

Water     .    . 

_ 

_ 

.002 

I 

" 

— 

0 

.00120 

2 

"         .    . 

- 

9-15 

.00136 

2 

- 

4 

.OOI29 

3 

- 

30 

.00157 

4 

*" 

18 

.00124 

5 

Solutions  in 

water. 

CuSO4    , 

1.160 

44 

.OOIlS 

2 

KC1    .    .    . 

1.026 

.OOIl6 

4 

NaCl  .    .    . 

33?% 

10-18 

.00267 

6 

H2SO4    .    . 

M 

1.054 

1.  100 

20.5 
20.5 

.OOI26 
.00128 

5 
5 

1.180 

21 

.OOI3O 

5 

ZnSO4     .     . 

1.134 

4-5 

.OOIl8 

2 

'     ' 

1.136 

4-5 

.00115 

2 

i  Bottomley.                4  Graetz. 

2  H.  F.  Weber.           5  Chree. 

3  Wachsmuth.             6  Winkelmann. 

TABLE  199.  —  Organic  Liquids. 


TABLE  200.  — Oases. 


Substance. 

( 

* 

a 

*c 

o 

o 

Acetic  acid  .    .    . 

9-1  5 

.472 

_ 

I 

Alcohols:  amyl    . 

•328 

- 

I 

ethyl    . 

9—15 

•423 

— 

I 

methyl 

9-15 

•495 

- 

I 

Benzole   .... 

5 

•333 

— 

I 

Carbon  disulphide 
Chloroform  .    .    . 

9-15 

•343 
.288 

— 

I 

I 

Ether  

9~I5 

•3°3 

— 

I 

Glycerine     .    .    . 

9-1  5 

.637 

O.I2 

2 

Oils  :  olive  .     .     . 

•39  S 

- 

3 

castor      .     . 

— 

•425 

— 

petroleum    . 

13 

•355 

O.OII 

2 

turpentine   . 

*3 

•325 

0.0067 

2 

Vaseline  .... 

•44 

"^ 

4 

i  H.  F.  Weber.          3  Wachsmuth. 

2  Graetz.                     4  Lees. 

Substance. 

t 
o 

kt 

Xioooo 

a 

Authority.  1  1 

Air     

0 
0 

.568 

.00190 
.OO26O 

I 
2 

Argon    .... 

Ammonia  .     .    . 

o 

•458 

.00548 

I 

Carbon  monoxide 

0 

•499 

_ 

I 

"      dioxide    . 

0 

•307 

- 

I 

Ethylene    .     .     . 
Helium  .... 
Hydrogen  .     .     . 

0 
0 
0 

•395 
3-39 
3-27 

.00445 
.00318 
.00175 

I 

2 

Methane     .    .     . 

7-8 

.647 

- 

1 

Nitrogen     .     .    . 
Nitrous  oxide 
Oxygen  .... 

7-8 
7-8 
7-8 

•524 

38 

.00446 

I 
I 

i  Winkelmann. 

2  Schwarze. 

*  Herschel,  Lebour,  and  Dunn  (British  Association  Committee). 


SMITHSONIAN  TABLES. 


TABLE  201 . 
HEAT   OF  COMBUSTION. 

Heat  of  combustion  of  some  common  organic  compounds. 
Products  of  combustion,  CO2  or  SO2  and  water,  which  is  assumed  to  be  in  a  state  of  vapor. 


2O I 


Substance. 

Small  calories 
per  gramme 
of  substance. 

Authority. 

IIQ27 

Thomsen. 

Alcohols  :  Amyl 

*  •*;'•'•  J 
8958 

Favre  and  Silbermann. 

Ethyl 

7183 

«<       <i              « 

Methyl       . 

5307 
0077 

(I              U                           «« 

Stohmann,  Kleber,  and  Langbein. 

Coals  :  Bituminous     . 

XX  /  / 

7400-8500 

Various. 

Anthracite     . 

7800 

Average  of  various. 

Lignite  .... 

6900 

«         «       <t 

Coke      .... 

7000 

«         «       n 

Carbon  disulphide 

3244 

Berthelot. 

Dynamite,  75  %  .... 

1290 

Roux  and  Sarran. 

Gas  :  Coal  gas   .... 

5800-11000 

Mahler. 

Illuminating 

5200-5500 

Various. 

Methane   .... 

13063 

Favre  and  Silbermann. 

Naphthalene 

9618-9793 

Various. 

Gunpowder         .... 

720-750 

« 

Oils  :  Lard         .        ... 

9200-9400 

« 

Olive         .... 

9328-9442 

Stohmann. 

Petroleum,  Am.  crude 

11094 

Mahler. 

"             "    refined   . 

11045 

M 

"          Russian  . 

10800 

U 

Woods  :  Beech  with  12.9%  H2O 

4168 

Gottlieb. 

Birch    «     11.83      " 

4207 

« 

Oak      «     13.3 

3990 

«i 

Pine      "     12.17      " 

4422 

« 

SMITHSONIAN  TABLES. 


2O2  TABLE  202. 

HEAT  VALUES  AND  ANALYSES  OF  VARIOUS  TYPES  OF  FUEL. 

(a)  Goals. 


Coal. 

Moisture. 

11 

|J 

4 

I 

CO 

Hydrogen.  I 

J 

C 

i 

K 

6 

j! 

B.  T.  U.'s 
per  pound.  1 

(Low  grade. 

38.81 

25.48 

27.29 

8.42 

.97 

7.09 

37-45 

•50 

45-57 

3526 

6347 

igni  e  -j  j-jjgh  grade  . 

33.38 

27.44 

29.62 

9-56 

•94 

6.77 

.67 

40.75 

3994 

7189 

Sub-bitu-  (  Low  grade    . 
minous  (  High  grade  . 

22.71 

15-54 

34-78 
33-03 

36.60 
46.06 

5.91 
5-37 

.29 

.58 

6.14 
5.89 

52.54 
60.08 

1.03 
1.05 

34.09 
27.03 

5IJ5 
S865 

9207 
10557 

Bituminous  j  Hh^grade 
Semi-bitu-  (  Low  grade  . 
minous    (  High  grade  . 

11.44 
3-42 
2.7 
3.26 

33-93 

14-5 
14-57 

43-92 
58.83 

75-5 
78.20 

10.71 
3-39 
7-3 
3-97 

4-94 
.58 

•99 

•S4 

5-39 

5-25 
4.58 
476 

60.06 
77.98 
80.65 
84.62 

1.02 
1.29 
1.82 
I.  O2 

17.88 

4.66 
5.09 

6088 
7852 

7845 
8166 

10958 

I4I34 
I4I2I 
14699 

Semi-anthracite.     .     .     . 

2.07 
2,76 

9.81 
2.48 

78.82 
82.07 

9-3° 
12.69 

1.74 

3-62 
2.23 

80.28 
79.22 

1.47 

.68 

3-59 
4.64 

7612 
6987 

13702 
12577 

n    ra  i     |  High  grade 

3-33 

3-27 

84.28 

9.12 

.60 

3.08 

81-35 

-79 

5.06 

7417 

(D)  Feats  (air  dried). 


From 

Vol. 
Hydro- 
Carbon. 

Fixed 
Carbon. 

Ash. 

Sul- 
phur. 

Hydro- 
gen. 

Carbon. 

Nitro- 
gen. 

Oxygen. 

Calories 
per 
gramme. 

B.T.U.'s 
per 
pound. 

Franklin  Co.,  N.  Y. 
Sawyer  Co.,  Wis. 

67.10 
56.54 

28.99 
27.92 

3-91 

15-54 

•'5 

.29 

5-93 

4.71 

57-17 
51.00 

1.48 
1.92 

3I-36 
26.54 

5726 
4867 

10307 
8761 

(o)  Liquid  Fuels. 


Fuel. 

Specific  Gravity 
at  15°  C 

Calories  per  gramme. 

British  Thermal  Units 
per  pound. 

Petroleum  ether  

.684-.694 

.7IO-.77O 

I22IO-I222O 
IIIOO-II4OO 

21978-21996 
19980-20520 

Kerosene     ....... 

.7QO—  5OO 

IIOOO-II2OO 

19800-20160 

Fuel  oils,  heavy  petroleum  or 

.q6o-.Q7O 

IO2OO—IO5OO 

18360-18900 

Alcohol,   fuel    or   denatured 
with  7-9  per  cent  water  and 
denaturing  material  .     .     . 

.8I96-.8202 

6440-6470 

11592-11646 

Table  compiled  by  U.  S.  Geological  Survey. 


SMITHSONIAN  TABLES. 


TABLE  203.  203 

CHEMICAL  AND  PHYSICAL   PROPERTIES  OF  FIVE   DIFFERENT  CLASSES 

OF  EXPLOSIVES. 


Explosive. 

Specific  gravity. 

Number  of  large  calories  developed  I 
by  i  kilogramme  of  the  explosive.  1 

Pressure  developed  in  own  volume  1 
after  elimination  of  surface  in- 

fluence. 

Unit  disruptive  charge  by  ballistic  1 
pendulum. 

Rate  of  detonation. 
Cartridges  ij  in.  diam. 

] 
B 

§« 

II 
^"3. 

Eg 

f  ° 
"o 

C 
.0 

8 

V 

•JJ 

ja 

4 
EL 
1 

1-s 

•11 

11 

•«« 

f 
£ 

C* 

o 

Products  of  combustion  from  200 
grammes  ;  gaseous,  solid,  and  liq-  1 
uid,  respectively. 

« 

a 
E 
-§•5 

1* 

ti 

l'§ 

v  In 

I1 

1 

Kg.  per 
sq.  cm. 

Grammes. 

u   8 

« 

li 

i  ° 

t 

J 

1 

C 

Grammes. 

o 

(A)  Forty-per-centnitro- 
glycerin  dynamite 

(B)  FFF  black  blasting 
powder 

(C)  Permissible      explo- 
sive; nitroglycerin 
class 

(D)  Permissible     explo- 
sive ;    ammonium 
nitrate  class 

(E)  Permissible     explo- 
sive; hydrated  class 

1.22 
1.25 
I.IO 

0.97 

i-54 

I22I.4 
789.4 
760.5 
992.8 
6lO.6 

8235 
4817 
5912 
7300 
6597 

227* 

374t 
458* 

301* 
279* 
434* 

4688 

4694* 
3008 

3438§ 
2479 

.358 
.925 
.471 

.483 

.338 

24.63 

54.32 
27.79 
25.68 
17.49 

12 

4 

i 

3 

88.4 
79-7 
14-5 

1544 
126.9 

4-  1  II 

103.9 
65-1 
154 

89.8 
27.5 

75-5 

86.1 
56.0 
33-o 

25 
25 

IOOO 

800 

Over 

IOOO 

Chemical  Analyses. 

(A)  Moisture    

0.91 
39.68 
42.46 
13.58 

3-37 

0.80 
70.57 

17.74 
10.89 

7.89 
24.02 
36-25 

9.20 
21.31 
0.97 
0.36 

(D) 
(E)l 

Vloistun 
Ammon 
Sulphur 
Starch 
Woodp 
Poisono 
Vfangan 
Sand 

Moisture 
^itrogly 
Ammon 
Sand 

1 

0.23 
83.10 

0.46 
2.61 

1.89 

2.54 

2.64 

6.53 

2.34 

30.85 

9-94 
1.75 
11.98 
7.64 
8.96 
6.89 
19.65 

Nitroglycerin       .          .          . 

ium  nitrate 

Sodium  nitrate             .         .     . 

Calcium  carbonate  
(B)  Moisture     

ulp 
us  ma 
sse  p< 

ttter    

;roxide 

Sodium  nitrate   

(C)  Moisture     

cerin 
mm  n 

itrate 

Nitroglycerin  

Sodium  nitrate    

Coal.     .     . 

Clay. 

Wood  pulp  and  crude  fibre  from 

*    

Ammonium  sulphate 
Zinc  sulphate  (7HO) 
Potassium  sulphate 



Starch    

Calcium  carbonate      .         .         . 



*  One  pound  of  clay  tamping  used.  t  Two  pounds  of  clay  tamping  used.  t  Rate  of  burning. 

§  Cartridges  i  J  in.  diam.  ||  For  300  grammes. 

Compiled  from  U.  S.  Geological  Survey  Results,  —  "  Investigation  of  Explosives  for  use  in  Coal  Mines,  1909." 
SMITHSONIAN  TABLES. 


2O4 


TABLE  204. 


HEAT  OF 


Heat  of  combination  of  elements  and  compounds  expressed  in  units,  such  that  when  unit  mass  of  the  substance  is 

units,  which  will  be  raised  in  temperature 


Substance. 

Combined 
with  oxygen 
forms  — 

Heat 
units. 

Combined 
with  chlorine 
forms  — 

Heat 
units. 

Combined 
with  sulphur 
forms  — 

Heat 
units. 

a£ 
<•« 

Calcium    . 

CaO 

3284 

CaCl2 

4255 

CaS 

2300 

I 

Carbon  —  Diamond, 

C02 

7859 

- 

- 

- 

2 

«                  « 

CO 

2141 

— 

— 

— 

— 

3 

"      —  Graphite 

CO2 

7796 

_ 

_ 

_ 

_ 

3 

Chlorine   . 

C12O 

—  254 

_ 

_ 

_ 

_ 

i 

Copper      .        . 

Cu2O 

321 

CuCl 

C20 

_ 

_ 

i 

" 

CuO 

585 

CuCl8 

819 

CuS 

IS8 

i 

« 

« 

593 

— 

— 

— 

4 

Hydrogen* 

H2O 

34154 

HC1 

22000 

H2S 

2250 

3 

u 

« 

34800 

- 

- 

- 

- 

5 

"         •  ;     •''  » 

« 

34417 

— 

— 

— 

— 

6 

FeO 

ITCI 

FeCl2 

1464 

FeSH2O 

428 

•7 

« 

O  DO 

FeCl3 

T^T" 
1714 

J 

3 

Iodine 

I205 

177 

— 

— 

— 

Lead 

PbO 

243 

PbCl2 

400 

PbS 

98 

Magnesium 
Manganese 

MgO 
MnOH2O 

6077 
1721 

MgCl2 
MnCl2 

6291 

2O42 

MgS 
MnSH2O2 

3T9i 
841 

Mercury    . 

Hg20 

105 

HgCl 

206 

- 

- 

t< 

HgO 

i53 

HgCl2 

3IO 

HgS 

84 

Nitrogen* 

N2O 

-654 

- 

- 

a 

NO 

—1541 

— 

— 

— 

— 

a 

N02 

—  143 

- 

- 

- 

- 

Phosphorus  (red) 

P206 

5272 

- 

- 

- 

- 

«             (yellow) 

M 

5747 

— 

— 

— 

— 

7 

«                   « 

« 

5964 

— 

— 

— 

— 

i 

Potassium 

K2O 

1745 

KC1 

2705 

K2S 

1312 

8 

Silver 
Sodium 

Ag2O 
Na2O 

27 
3293 

AgCl 
NaCl 

271 
4243 

Ag2S 
Na2S 

24 
1900 

i 
8 

Sulphur 

SO2 

2241 

- 

- 

- 

i 

« 

« 

2165 

— 

— 

— 

— 

2 

Tin    . 

SnO 

573 

SnCl2 

60X> 

- 

- 

4 

« 

SnCl4 

Tn&n 

_^ 

mm 

7 

Zinc  

ZnO 

iiSq 

_ 

_ 

_ 

/ 

4 

u 

« 

D 

1714 

ZnCl2 

I4QC 

_ 

_ 

i 

o  ^ 

"•tyj 

Substance. 

Combined 
withS-fO4 
to  form  — 

Heat 
units. 

Combined 
with  N  +  O, 
to  form  — 

Heat 
units. 

Combined 
withC  +  O, 
to  form  — 

Heat 
units. 

1* 

Calcium     . 

CaSO4 

7997 

Ca(N03)2 

5080 

CaC08 

6730 

Copper 

CuSO4 

2887 

Cu(NO3)2 

I3°4 

— 

— 

Hydrogen 

H2S04 

96450 

HN03 

41500 

— 

— 

FeSO4 

4208 

Fe(NO3)2 

2  1  "34 

_ 

_ 

Lead 

PbS04 

1047 

Pb(N03)2 

AXOT" 

512 

PbC03 

814 

Magnesium 

MgS04 

12596 

- 

Mercury    . 

— 

— 

— 

— 

— 

Potassium 

K2S04 

4416 

KNO3 

3061 

K2C03 

3583 

Silver 
Sodium 

Ag2S04 
Na2SO4 

776 
7119 

AgN03 
NaNO3 

266 
4834 

Ag2C03 
Na2CO8 

56l 

5841 

ZnSO4 

<?cr?8 

«. 

_ 

J  J«5" 

AUTHORITIES. 

i  Thomsen.       3  Favre  and  Silberrnann.    5  Hess.                                        7  Andrews. 

2  Berthelot.       4  Joule.                                6  Average  of  seven  different.     8  Woods. 

SMITHSONIAN  TABLES. 


Combustion  at  constant  pressure. 


TABLE  204  (continue*). 


205 


COMBINATION. 


caused  to  combine  with  oxygen  or  the  negative  radical,  the  numbers  indicate  the  amount  of  water,  in  the 
from  o°  to  i°  C.  by  the  addition  of  that  heat. 


In  dilute  solutions. 

A 

Substance. 

Forms  — 

Heat 
units. 

Forms  — 

Heat 

units. 

Forms  — 

Heat 
units. 

!•* 

Calcium 
Carbon  —  Diamond 

CaOH2O 

3734 

CaCl2H2O 

4690 

CaS  +  H20 

2457 

i 

2 

a                  « 

_ 

_ 

_ 

_ 

„ 

_ 

3 

"      —  Graphite 

- 

- 

- 

- 

- 

- 

3 

Chlorine    . 

_ 

— 

— 

_ 

_ 

_ 

i 

Copper       .        .  _( 

_ 

_ 

— 

— 

— 

— 

i 
i 

•        •        * 

— 

— 

— 

— 

— 

— 

4 

Hydrogen  . 

- 

- 

- 

- 

- 

- 

3 

« 

: 

: 

I 

: 

: 

~ 

1 

Iron   . 

FeO+H20 

1  220* 

FeCl2  +  H2O 

1785 

- 

- 

3 

" 

— 

— 

FeCl8 

2280 

_ 

— 

3 

Iodine        .        . 

_ 

_ 

_ 

_ 

_ 

_ 

Lead  . 

_ 

- 

PbCl2 

368 

_ 

_ 

Magnesium 

Mg02H2 

9050  1 

MgCl2 

7779 

MgS 

4784 

Manganese 

— 

MnCl2 

2327 

_ 

Mercury     . 

- 

- 

- 

- 

- 

"           .        . 

— 

— 

HgCla^ 

299 

— 

— 

Nitrogen   . 

_ 

— 

— 

: 

Phosphorus  (red) 

_ 

_ 

— 

: 

; 

— 

(yellow) 

- 

- 

- 

- 

- 

- 

7 

«                  « 

— 

— 

_ 

_ 

_ 

_ 

i 

Potassium 

K2O 

2  no* 

KC1 

2592 

K2S 

I451 

8 

Silver 

_ 

_ 

_ 

_ 

_ 

j 

Sodium 

Na20 

3375 

NaCl 

4190 

Na2S 

2260 

8 

Sulphur 

- 

- 

- 

- 

- 

i 

. 

— 

— 

— 

— 

— 

— 

2 

Tin    . 

- 

- 

SnCl2 

691 

_ 

_ 

7 

" 

- 

- 

SnCl4 

1344 

- 

- 

7 

Zinc  . 

— 

— 

— 

— 

— 

4 

• 

~ 

— 

ZnClj 

1735 

— 

— 

i 

In  dilute  solutions. 

| 

Substance. 

Forms  — 

Heat 

units. 

Forms  — 

Heat 
units. 

Forms  — 

Heat 
units. 

!& 

Calcium 

_ 

- 

Ca(N03)2 

5*75 

_ 

_ 

Copper 
Hydrogen 

CuS04 
H2S04 

3150 
105300 

Cu(N08)2 
HNO, 

1310 

2455° 

_ 

_ 

Iron  . 

FeSO4 

4210 

Fe(N03)3 

2134 

— 

— 

Lead. 

_ 

— 

Pb(N03)2 

475 

— 

— 

Magnesium 
Mercury 
Potassium 

MgS04 
K2SO4 

13420 
4324 

Mg(N03)2 
Hg(N03)2 
KNOs 

8595 

- 

- 

Silver 
Sodium 

Ag2SO4 
Na2S04 

753 
7160 

AgN03 
NaNO3 

216 
4620 

Na2CO8 

5995 

Zinc  . 

ZnSO4 

3820 

Zn(N03)2 

2035 

— 

AUTHORITIES. 

i  Thomsen.        3  Favre  and  Silbermann.      5  Hess.                                        7  Andrews. 

2  Berthelot        4  Joule.                                  6  Average  of  seven  different.    8  Woods. 

*  Thomsen. 


f  Total  heat  from  elements. 


SMITHSONIAN  TABLES. 


206 


TABLE  205. 
LATENT  HEAT  OF  VAPORIZATION, 


The  temperature  of  vaporization  in  degrees  Centigrade  is  indicated  by  T;  the  latent  heat  in  large  calories  per  kilo- 
gramme or  in  small  calories  or  therms  per  gramme  by  H ;  the  total  heat  from  o°  C.  in  the  same  units  by  H'.  The 
pressure  is  that  due  to  the  vapor  at  the  temperature  T. 


Substance. 

Formula. 

T 

H 

H* 

Authority. 

Acetic  acid  .... 

C2H4O2 

118° 

84.9 

- 

Ogier.    ' 

Air                                * 

— 

_ 

CO.Q7 

Fenner-Richtmyer. 

Alcohol:  Amyl    « 

C6H120 

131 

Jx/ 

1  20 

- 

Schall. 

Ethyl   . 

« 

C2H60 
(i 

78.1 
o 

205 
236 

255 
236 

Wirtz. 
Regnault. 

ii 

it 

5° 

264 

" 

ii 

ii 

100 

— 

267 

ii 

« 

ii 

ISO 

- 

285 

<i 

Methyl  . 
it 

CH40 

« 

64.5 
o 

2.67 
289 

307 
289 

Wirtz. 
Ramsay  and  Young. 

• 

ii 

5° 

274 

«          « 

«i 

ii 

100 

_ 

246 

K          <i 

i< 

ii 

J5° 

- 

206 

ii          ii 

« 

" 

200 

_ 

J52 

II                   !< 

i< 

ii 

238.5 

- 

44.2 

II                   II 

Ammonia     .... 

NH3 

7.8 

294.2 

- 

Regnault. 

it 

«« 

ii 

291.3 

— 

« 

ii 

ii* 

16 

297.4 

— 

ii 

it 

ii 

17 

296.5 

- 

H 

Benzene       .... 

C6H6 

80.  i 

92.9 

127.9 

Wirtz. 

Bromine        .... 

Br 

61 

45-6 

- 

Andrews. 

Carbon  dioxide,  solid  . 

CO2 

_ 

_ 

138-7 

Favre. 

"            "         liquid 

M 

—25 

72.23 

Cailletet  and  Mathias. 

<i            <«             <i 

II 

0 

5748 

— 

«         ii         ii 

«            it             i< 

II 

I2-35 

44-97 

- 

Mathias. 

ii            ii            « 

(( 

.    22.04 

31-8 

— 

N 

<«                      «                       « 

l( 

29.85 

14.4 

— 

M 

II                      II                       II 

II 

30.82 

3-72 

- 

II 

«!      disulphide 

CS8 

II 

46.1 

0 

83.8 
90 

94.8 
90 

Wirtz. 
Regnault. 

<«             « 

It 

100 

100.5 

« 

««             « 

II 

140 

- 

102.4 

u 

Chloroform  .... 

CHC13 

60.9 

58.5 

72.8 

Wirtz. 

Ether    

C4Hi0O 

-34.  e 

884 

1  07 

ii 

<c 

V^£.L  A  Jig  ^J 
II 

«JT"  J 
•\A    Q 

tjw.if. 

QO  S 

/ 

Andrews. 

«i 

II 

3*t'y 

o 

Sn*j 

Qd. 

QA 

Regnault. 

« 

II 

SO 

y't 

7T- 
II5.I 

ic 

II 

1  2O 

IAO 

ii 

I 

21  QC 

l^U 

Favre  and  Silbermann. 

Mercury       .... 

Hg 

357 

•^j-yo 
65 

- 

Mean. 

Nitrogen      .... 

'N 

—195.6 

47.65 

- 

Alt. 

Oxygen         .... 

0 

—182.9 

50.97 

- 

« 

Sulphur  dioxide   .        . 

S02 

0 

91.2 

_ 

Cailletet  and  Mathias. 

«            (i 
ii            « 

II 
l< 

i: 

80.5 
68.4 

- 

it         it          ii 
ii         «i          ii 

Turpentine  .        .        .        . 

CioHio 

r59-3 

74-°4 

- 

Brut. 

Water  

H2O 

IOO 

C-7C.Q 

_ 

Andrews. 

ii 

ii 

IOO 

Jjj  7 

«&7 

Regnault. 

SMITHSONIAN  TABLES. 


TABLE  205  (continued). 


207 


LATENT   HEAT  OF   VAPORIZATION.* 


Substance,  formula,  and 
temperature. 

1=  total  heat  from  fluid  at  o°  to  vapor  at  /°. 
r=  latent  heat  at  t°. 

Authority. 

Acetone, 
C8H60, 

-3°toi47°- 

/=  140.5  -j-  0.36644  /  —  0.00951  6/2 
'  =  J39-9  +  0.23356  1  +  0.00055358  ft 
r  =  139.9  —  0.27287  /  -j-  0.0001571  12 

Regnault. 
Winkelmann. 

M 

Benzene, 
C6H6, 

7°  to  215°. 

/=  109.0  +  0.24429  /  —  0.000131  5^ 

Regnault. 

Carbon  dioxide, 
C02, 

—  25°  to  31°. 

r*=  1  18.485  (31  —  t)  —  0.4707  (31  —  fy 

Cailletet  and 
Mathias. 

Carbon  disulphide, 
CS2, 
—  6°  to  143° 

7  =  90.0  +  0.14601  1  —  0.000412/2 
/  =  89.5  -j-  0.16993  /  —  0.0010161  £2  +  0.000003424  /* 
r  =  89.5  —  0.06530  1  —  0.0010976  /2  -j-  0.000003424  fl 

Regnault. 

Winkelmann. 
« 

Carbon  tetrachloride, 

ecu, 

8°  to  163°. 

1=  52.0  +  0.14625  /  —  6.000172  fi 
1  =  5  1  .9  +  o.  1  7867  t  —  0.0009599  /2  +  0.000003733  /* 
r  =  51.9  —  0.01931  /  —  0.0010505  /2  -f  0.000003733  fl 

Regnault. 
Winkelmann. 

H 

Chloroform, 
CHC13, 
-5°  to  159°. 

7=67.0  +  0.1375  1 
7  =  67.0  +  0.147  16/  —  0.0000937  fl 
r  =  £f].Q  —  0.08519  1  —  0.0001444  fl 

Regnault. 
Winkelmann. 

M 

Nitrous  oxide, 
N2O, 
—  20°  to  36°. 

r*=  131.75  (364  —  0—0.928  (364  —  /)2 

Cailletet  and 
Mathias. 

Sulphur  dioxide, 
S02, 
o°  to  60°. 

r  =   91  .87  —  0.3842  1  —  0.000340  fl 

Mathias. 

*  Quoted  from  Landolt  and  Boernstein's  "  Phys.  Chem.  Tab."  p.  350. 
SMITHSONIAN  TABLES. 


208 


TABLE  206. 
LATENT    HEAT    OF    FUSION, 


This  table  contains  the  latent  heat  of  fusion  of  a  number  of  solid  substances  in  large  calories  per 
kilogramme  or  small  calories  or  therms  per  gramme.  It  has  been  compiled  principally  from 
Landolt  and  Bernstein's  tables.  C  indicates  the  composition,  T  the  temperature  Centigrade, 
and  //the  latent  heat. 


Substance. 

C 

T' 

H 

Authority. 

Alloys:  3o.5Pb  +  69-5Sn   . 
36.9Pb-j-  63.iSn   . 
63.7Pb  +  36.3Sn    . 
77.8Pb-f22.2Sn    . 
Britannia  metal,  pSn  -f-  iPb 
Rose's  alloy, 
24Pb+27.3Sn  +  48.7Bi 
Wood's  a,loy|¥.8Pb+;4,Sn| 

PbSn4 
PbSn3 
PbSn 
Pb2Sn 

Al 

183 
179 

177.5 
176.5 
236 

98.8 

75-5 
6c8. 

17- 

15.5 

1  1.6 

9-54 
28.0* 

6.85 
8.40 
768 

Spring. 
it 

« 
«« 

Ledebur. 

Mazzotto. 
H 

Glaser 

Ammonia   

NH8 
C6H6 

—75- 

c.4 

108. 
"io  6 

Massol. 
Mean. 

Br 

7.  "I 

jw.w 
16  2 

Regnault. 

Bi 

768  3 

12.64 

Person. 

Cd 

72O.7 

i  ^  66 

Calcium  chloride 

CaCl2  +  6H20 
Cu 

28.5 

1087 

40.7 
42. 

<« 
Mean. 

Iron,  Gray  cast  .... 
"     White  "    . 
«'     Slag   

23- 
33- 

CQ. 

Gruner. 

H 

I 

II.  71 

Favre  and  Silbermann. 

Ice      

H2O 

o 

79.24 

Regnault. 

« 

o 

80.02 

Bunsen. 

"    (from  sea-water)          . 
Lead   

JH20  +  3.535l 
I      of  solids      \ 
Pb 

-8-7 

727 

54-o 
S.86 

Petterson. 
Rudberg. 

Hg 

—  39 

282 

Person. 

Naphthalene       .... 
Nickel         

.  CioH8 
Ni 

79-87 

I4TC 

3S.& 

4.64 

Pickering. 
Pionchon. 

Palladium    

Pd 

I  CAC 

*t-vtt 

-j6.i 

Violle. 

Phosphorus         .        .        . 

P 

Pt 

44.2 

I7CC 

4-97 
27.2 

Petterson. 
Violle. 

K 

*y  jj 
62 

15.7 

Joannis. 

Potassium  nitrate       .        . 
Phenol         

KN03 
C6H6O 

333-5 

2<v77 

48.9 

24.Q^ 

Person. 
Petterson. 

IJ2.4O 

^^.10 

Batelli. 

Silver          

Ag 

Na 

3-Mlw 

01 

97 

21.07 
31.7 

Person. 
Joannis. 

nitrate    .... 
"       phosphate     . 
Spermaceti          .... 

NaN03 
(  Na2HPO4  ) 
i  +  i2H20  f 

s 

305-8 
36-1 
43.9 

II  C 

64.87 

66.8 

36.98 
9-37 

u 

« 

Batelli. 
Person. 

Tin      
Wax  (bees)         .... 
Zinc    

Sn 
Zn 

232 
61.8 
419 

14-0 
42.3 
28.17 

Mean. 
«« 
<« 

*  Total  heat  from  o°  C. 


SMITHSONIAN  TABLES. 


TABLE  207. 
MELTING-POINTS  OF  THE   CHEMICAL   ELEMENTS. 


209 


The  metals  in  heavier  type  are  often  used  as  standards. 

The  melting-points  are  reduced  as  far  as  possible  to  a  common  temperature  scale  which  is  the 
one  used  by  the  United  States  Bureau  of  Standards  in  certifying  pyrometers.  This  scale  is  de- 
fined in  terms  of  Wien's  law  with  C  taken  as  14000,  and  on  which  the  melting-point  of  platinum 
is  1755°  C  (Nernst  and  Wartenburg,  1751 ;  Waidner  and  Burgess,  1753;  Holborn  and  Valentiner, 
1770;  see  C.  R.  148,  p.  1177,  1909).  Above  1100°  C,  the  temperatures  are  expressed  to  the 
nearest  5°  C.  Temperatures  above  the  platinum  point  may  be  uncertain  by  over  50°  C. 


Element. 

Melting- 
point. 

I  Remarks. 

Element. 

Melting- 
point. 

Remarks. 

Aluminum 

658^1 

Most      samples 

Manganese 

1225 

Adjusted. 

give  657  or  less 
(Burgess). 

Mercury 
Molybdenum 

—  39 

>2000 

Probably. 

Antimony 

630^1 

"Kahlbaum"  pu- 

Neodymium 

840 

(Muthmann-Weiss.) 

rity. 

Neon 

—  252 

Argon 

—  188 

Ramsay-Tra  vers  . 

Nickel 

I45«> 

Adjusted  (Day-Sos- 

Arsenic 

>Sb,  <Ag 

Under  pressure. 

man  =  1452). 

Barium 

850 

(Guntz.) 

Niobium 

1950 

v.  Bolton. 

Beryllium 
Bismuth 

<Ag. 
270 

Adjusted. 

Nitrogen 
Osmium 

—  211 

About  2700 

(Fischer-  Alt.) 
(Wraidner  -  Burgess, 

Boron 

(  >2000  ) 
\  <2500  J 

Weintraub. 

Oxygen 

—  230? 

unpublished.) 

Bromine 

—  7-3 

Palladium 

1545  ±^5 

(Waidner-Burgess, 

Cadmium 

321 

Range  :     320.7- 

Nernst-Warten- 

321.7 

burg.) 

Caesium 

26 

Range  :     26.37- 

Phosphorus 

44-2 

Calcium 

805 

25-3 
Adjusted. 

Platinum 
Potassium 

1755  ±20 
62.5 

See  Note. 

Chlorine 

—  102 

(Olszewski.) 

Praesodymium 

940 

(Muthmann-Weiss.) 

Carbon 

(>  3500) 

Sublimes. 

Rhodium 

1910 

(Mendenhall-Inger- 

Cerium 

(Muthmann- 

soll.) 

Weiss.) 

Rubidium 

38.5 

Chromium 

1505 

Adjusted. 

Ruthenium 

1900? 

Cobalt 

1490 

Day-Sosman. 

Samarium 

1300-1400 

(Muthmann-Weiss.) 

Copper 

1083^3 

Mean,  Holborn- 

Silicon 

1420 

Adjusted. 

Day,        Day- 

Silver 

961  J-  i 

Adjusted.     . 

Clement. 

Sodium 

97 

Erbium 

Strontium 

Between  Ca  and  Ba  ? 

Fluorine 

—  223 

(Moissan  -  De- 

Sulphur 

113.5-119.5 

Various  forms.     See 

war.) 

Landolt-Bornstein. 

Gallium 

30.1 

Tantalum 

2800 

Adjusted  from  Waid- 

Germanium 

<Ag 

ner-Burgess  =  2910. 

Gold 

1063^3 

Adjusted. 

Tellurium 

451 

Adjusted. 

Hydrogen 

—  259 

Thallium 

301 

Indium 

155 

(Thiel.) 

Thorium 

>i7oo<Pt 

v.  Wartenburg. 

Iodine 

114 

Range:  112-115. 

Tin 

231.9  ^  .2 

Iridium 

(>2250) 
1  <2300  f 

Adjusted. 

Titanium 
Tungsten 

2950 

Above  2000? 
Mean,  Waidner-Bur- 

Iron 

1520 

Adjusted. 

gess  and  Warten- 

Krypton 

-I69 

(Ramsay.) 

burg. 

Lanthanum 

810 

(Muthmann- 

Uranium 

Near  Mo 

Moissan. 

Weiss.) 

Vanadium 

175° 

Vogel-Tammann. 

Lead 

327^-0.5 

Xenon 

—  140 

Ramsay. 

Lithium 

186 

(Kahlbaum.) 

Zinc 

Magnesium 

651 

(Grube)  in  clay 

Zirconium 

>Si 

Troost. 

crucibles,  635. 

SMITHSONIAN  TABLES. 


2IO 


TABLE  208. 
BOILING-POINTS  OF  THE  CHEMICAL  ELEMENTS. 


Element. 

Range. 

Boiling- 
point. 

Observer;  Remarks. 

Aluminum 

o 

0 

1800. 

Greenwood,  Ch.  News,  100,  1900. 

Antimony 

- 

1440. 

«                          4<                  «                «             «l 

Argon 
Arsenic 

449-450 

—I86.I 

Ramsay-Travers,  Z.  Phys.  Ch.  38,  1901. 
Gray,  sublimes,  Conechy. 

« 

280-310 

>36o. 

Black,  sublimes,  Engel,  C.  R.  96,  1883. 
Yellow,  sublimes. 

Barium 

— 

— 

Boils  in  vacuo,  Guntz,  1903. 

Bismuth 

1420-1435 

1430. 

Barus,  1894;  Greenwood,  1.  c. 

Boron 

Volatilizes  without  melting  in  electric  arc. 

Bromine 

59-63 

61.1 

Thorpe,  1880  ;  van  der  Plaats,  1886. 

Caesium 

670. 

Ruff-Johannsen. 

Carbon 

- 

3600. 

Computed,  Violle,  C.  R.  120,  1895. 

« 
Cadmium 

760-782 

770. 

Volatilizes  without  melting  in  electric  oven,  Moisson. 

Chlorine 
Chromium 

— 

-33-6 

22OO. 

Regnault,  1863. 
Greenwood,  Ch.  News,  100,  1909. 

Copper 

2100-2310 

23IO. 

1.  c. 

Fluorine 

— 

-I87. 

Moisson-Dewar,  C.  R.  136,  1903. 

Helium 
Hydrogen 

—252.5-252.8 

-267. 
—  252.6 

Computed,  Tracers,  Ch.  News,  86,  1902. 
Mean. 

Iodine 

— 

>200. 

Iron 

- 

2450. 

Greenwood,  1.  c. 

Krypton 

- 

—151-7 

Ramsay,  Ch.  News,  87,  1903. 

Lead 

— 

J525- 

Greenwood,  1.  c. 

Lithium 

- 

1400. 

Ruff-Johannsen,  Ch.  Ber.  38,  1905. 

Magnesium 

— 

1  1  20. 

Greenwood,  1.  c. 

Manganese 

— 

1900. 

«            « 

Mercury 

- 

357- 

Crafts  ;  Regnault. 

Nitrogen 

—195.7-194.4 

—  !95- 

Mean. 

Oxygen 

—182.5-182.9 

—182.7 

M 

Ozone 

— 

—  119. 

Troost,  C.  R.  126,  1898. 

Phosphorus 

287-290 

288. 

Potassium 

667-757 

712. 

Perman  ;  Ruff-Johannsen. 

Rubidiom 

696. 

Ruff-Johannsen. 

Selenium 

664-694 

690. 

Silver 

!955' 

Greenwood,  1.  c. 

Sodium 

742-757 

750- 

Perman;  Ruff-Johannsen. 

Sulphur 

444.7-445 

444-7 

Mean. 

Tellurium 

1390. 

Deville-Troost,  C.  R.  91,  1880. 

Thallium 

1600-1800 

1700. 

Tin 

_ 

2270. 

Greenwood,  1.  c. 

Xenon 

- 

—  109.1 

Ramsay,  Z.  Phys.  Ch.  44,  1903. 

Zinc 

916-942 

930. 

SMITHSONIAN  TABLES. 


TABLE  209. 
MELTING-POINTS  OF  VARIOUS  INORGANIC  COMPOUNDS.* 


211 


Substance. 

Chemical  Formula. 

Melting-point. 

Authority.  1 

Date  of 
Publication. 

Min. 

Max. 

Particular 
or  Average 
Value. 

Aluminum  chloride      .    . 
nitrate  .     .     . 

A1C18 
A1(N08)3  +  9H20 
NH8 
(NH4NO8 
(NH4)2S04 
NH4H2P08 
SbH8 
SbCl8 
SbCl5 
AsCl8 
AsH8 
Ba(C108)2 
Ba(N08)2 
Ba(C104)2 
BiCl8 
H8B08 
B2O3 
Na2B4O7 
CdCl2 
Cd(N03)2  +  4H20 
CaCl2 
CaCl2  +  6H2O 
Ca(N03)2 
Ca(NO3)2  +  4H2O 
CC14 
C2Cl<j 
CO 
C02 
CS2 
HC1O4+H2O 
C102 
KCr(SO4)2+i2H2O 
Cr2(NO3)6  -f  i8H2O 
CoSO4 
CuCl2 
Cu2Cl2 
Cu(N03)2  +  3H20 
HBr 
HC1 
HF1 
HI 
H2O2 
PH8 
H2S 
FeCl3 
Fe(N08)3  +  9H20 
FeSO4-f  7H2O 
PbCl2 
Pb(P08)2 
MgCl2 
Mg(N03)2  +  6H20 
MgS04  +  sH20 
MnCl2  +4H2O 
Mn(NO3)2  +  6H2O 
MnSO4  +  5H2O 
HgCl2 

MS- 

72. 

225. 
I84. 

719. 
499- 

182. 
-199. 
-56.5 

96. 

49-5 

301. 
447- 

287. 

166. 
73-2 

'& 

878. 
590. 

806. 

187. 
—207. 

—57-5 
98. 

Si«3 

307. 
580. 

293- 

190. 

72.8 

—75- 
156. 
140. 
123. 
-91-S 

-3* 

—  18. 

—"3-5 
414. 

593- 
5°5- 
227.5 

185. 
577- 
561. 
54i. 

59-5 
762 
29.6 
561. 
44. 
—24.7 
184.5 
-  203. 

—1  12^8 

5°. 
—76. 
89. 
37- 

434- 
II4-S 
—86.7 
—111.3 
—92.3 
51-3 

--5 

303- 

47-2 
64. 
coo. 
800. 
708. 
90. 

fe 

25.3 

54- 
290. 

I 

2 
3 

4 

I 
\ 

6 
9 
9 
10 
ii 
9 
9 
9 
9 

2 

9 

2 
12 

3 

14 
15 

16 

2 

16 
9 
9 

2 

'! 
g 

6 
3 

2 

16 

9 
9 

2 

16 

!9 

2 

16 

1888 
1859 
1875 

1837 
1887 
1886 

1875 
1903 
1884 
1878 
1878 
1884 
l876 
1878 
1878 
1878 
1878 
1859 

1878 
I859 
I863 

1845 
1903 

1861 

1845 
1884 

i859 
1884 
1878 
1878 
i859 
1845 

1900 

1886 
1845 

1859 
1884 

i8~78 
1878 

i8j9 
1884 

1859 
1884 

Ammonium  nitrate  .    .     . 
sulphate   .    . 
phosphite  .    . 
Antimonietted  hydrogen  . 
Antimony  trichloride  .     . 
"         pentachloride  . 
Arsenic  trichloride  .     .    .. 
Arsenietted  hydrogen  .    . 
Barium  chlorate  .... 
"       nitrate    .... 
"       perchlorate      .    . 
Bismuth  trichloride      .     . 
Boric  acid        .              .    . 

"      anhydride  .... 
Borax  (sodium  borate) 
Cadmium  chloride  .     .    . 
"         nitrate     .     .     . 

Calcium  chloride     .    .    . 
«               « 

"         nitrate  .... 
«             « 

Carbon  tetrachloride    .    . 
"       trichloride  .    .    . 
"       monoxide    .    .    . 
"       dioxide  .... 
"       disulphide  .    .    . 
Chloric  acid        .    .    •     . 

Chlorine  dioxide      .    .     . 

"       nitrate  .... 
Cobalt  sulphate  .... 
Cupric  chloride  .... 

"       nitrate  .... 
Hydrobromic  acid   ,    .    . 
Hydrochloric     "... 
Hydrofluoric     "... 
Hydroiodic        "... 
Hydrogen  peroxide      .     . 
"         phosphide  .     . 
"         sulphide.    .    . 
Iron  chloride       .... 

"     nitrate 

"     sulphate  

Lead  chloride      .     . 
"     metaphosphate 
Magnesium  chloride 
"          nitrate  . 
"          sulphate 
Manganese  chloride 
nitrate  . 
"          sulphate 
Mercuric  chloride    . 

i  Friedel  &  Crafts.    5  Amat.                9  Carnelley.                    13  Wroblewski  &        16  Tilden. 
2  Ordway.                  6  Olszewski.      10  Carnelley  &  O'Shea.          Olszewski.            17  Ladenburg. 
3  Faraday.                   7  Kammerer.     12  Regnault.                     14  Holborn  &  Wien.    18  Staedel. 
4  Marchand.              8  Baskerville.    n  Muir.                          15  Roscoe.                   19  Clarke,  "  Const,  of  Nat." 

*For  more  extensive  tables  on  this  subject,  see  Carnelley's  "  Melting  and  Boiling-point  Tablei,"  or  Landolt  and 
BSrnstein's  "  Phys.  Chem.  Tab." 

SMITHSONIAN  TABLES. 


212  TABLE 

MELTING-POINTS  OF  VARIOUS  INORGANIC  COMPOUNDS. 


Melting-point. 

Substance. 

Chemical  Formula. 

Min. 

Max. 

Particular 
or 
Probable 

f 

Date  of 

Publication  . 

Value. 

"* 

Nickel  carbonyl   .... 

NiCO4 

__ 

_ 

I 

1890 

"       nitrate  

Ni(NO8)2  +  6H2O 

_ 

_ 

Cn  i 

2 

1859 

"       sulphate    .... 

NiSO4  +  7H2O 

98. 

ICX). 

99. 

3 

1884 

HNO8 

_,  4  «T 

TC7Q 

"     anhydride  .... 

N206 

_ 

_ 

47- 

5 

lOyO 

1872 

"      oxide  *  

NO 

T  CO 

^ 

T^*7 

X 

Tco- 

"      peroxide    .... 

N204 

—9- 

—  12. 

—  10.6 

O 

IOO  R 

Nitrous  anhydride    .    .    . 

N203 

_ 

—82. 

7 

1889 

"       oxide  ..... 

N20 
H3P04 

38.6 

41.7 

—102.3 

8 

1893 

Phosphoric  acid  (ortho)    . 

Phosphorous  acid     .     .    . 

H8P08 

70.1 

74- 

72. 

_ 

_ 

Phosphorus  trichloride 

PC18 

1  1  1.8 

10 

1883 

"         oxychloride    . 

POC18 

_ 

_ 

i  t 

ii 

1871 

"         disulphide  .     . 
pentasulphide 
sesquisulphide 

P8S6 
P2S5 

296. 
274. 
142. 

298. 
276. 
167. 

297. 

12 
13 

I879 
I879 

"         trisulphide 

P2S3 

290. 

IA 

1864 

Potassium  carbonate     .    . 

K2CO3 

834- 

897. 

840. 

_ 

chlorate  .     .    . 

KC108 

334. 

360. 

_ 

— 

"         perchlorate  .    . 

KC104 

_ 

010. 

15 

1880 

chloride  .    .    . 

KC1 

740. 

804. 

779- 

_ 

nitrate     .     .    . 

KN08 

327. 

353. 

34° 

_ 

_ 

"         acid  phosphate 

KH2PO4 

**     >• 

96. 

3 

1884 

"         acid  sulphate    . 

KHSO4 

_ 

- 

200. 

16 

1840 

Silver  chloride      .... 

AgCl 

45°- 

460. 

455- 

_ 

_ 

nitrate    

AgN08 

198. 

224. 

214. 

_ 

_ 

nitrogenietted     .    . 
perchlorate     .     .     . 

AgN8 
AgC104 

250. 
486. 

\l 

1890 

phosphate  .... 

Ag3P04 

_ 

_ 

849. 

15 

1878 

metaphosphate  .    . 

AgP08 

- 

- 

482. 

15 

1878 

"      sulphate     .... 

Ag2S04 

654- 

676. 

665. 

_ 

Sodium  chloride  .... 

NaCl 

772. 

820. 

795- 

_ 

_ 

"       hydroxide    .    .    . 

NaOH 

- 

^*> 

60. 

19 

1884 

"       nitrate     .... 

NaNO8 

308. 

33°- 

3T5- 

_ 

"       chlorate  .... 

NaC108 

248. 

302. 

275- 

_ 

_ 

"       perchlorate.    .    . 

NaC104 

_ 

482. 

18 

1884 

"       carbonate    .    .    . 

Na2C08 

814. 

920. 

852. 

_ 

_ 

*               " 

Na2C03  +  ioH20 

_ 

_ 

34- 

3 

1884 

'        phosphate   .     .     . 
'        metaphosphate     . 

Na2HPO4  +  4H2O 
NaPO8 

35- 

364 

354 
617. 

15 

1878 

4        pyrophosphate 

Na4P2O7 

888. 

970. 

938- 

_ 

*        phosphite    .    .     . 

(H2NaP03)2  4  5H20 

_ 

42. 

20 

1888 

"       sulphate       .    .    . 

Na2SO4 

861. 

865. 

863. 

15 

1878 

"         .... 

Na2SO4  4-  ioH2O 

— 

34- 

3 

1884 

"       hyposulphite    .    . 
Sulphur  dioxide    .... 

Na«jS2O3  +  5H2O 
SO2 

45- 
73- 

48.1 
79- 

47- 
76. 

Sulphuric  acid      .... 

H2S04 

10.  1 

10.6 

10.4 

21 

1884 

<f                      U 

I2H2SO4  4  H2O 

_ 

^ 

—0.5 

22 

T  S  C  "J 

«                      « 

H2SO4  4  H2O 

7  5. 

8  c 

8. 

JJ 

/'(pyro).    .    . 

H2S2O7 

/O 

35- 

22 

l853 

Sulphur  trioxide  .... 

S08 

14.8 

15. 

14.9 

5 

1876-1886 

Tin,  stannic  chloride     .    . 

SnCl4 

- 

- 

—33- 

23 

1889 

"    stannous     "... 

SnCl2 

_ 

_ 

24 

_ 

ZnCl2 

_ 

_ 

262 

2  C 

1871 

ZnCl2  4  3H2O 

6  c 

26 

iu/  j 

"    nitrate      

Zn(NO3)2  4  6H2O 

uo 

•j 

1884 

"    sulphate  

ZnSO4  4  7H2O 

CO 

J 

i8sl 

5  ' 

* 

i  Mond,  Langer    5  R.Weber.   10  Wroblewski  &    13  V.  &  C.  Meyer.  18  Carnelley  &    22  Marignac. 
&  Quincke.     6  Olszewski.           Olszewski.         14  Lemoine.                      O'Shea.        23  Besson. 
2  Ordway.              7  Birhaus.       n  Genther&Mi-  15  Carnelley.            ig  Cripps.       24  Clarke,"  Const,  of  Nat." 

3  Tilden.                 8  Ramsay.               chaelis.               16  Mitscherlich.       20  Amat.                25  Braun. 

4  Berthelot.           9  Wills.            12  Ramme.              17  Curtius.               21  Mendelejeff.    26  Mylius. 

SMITHSONIAN  TABLES. 


*  Under  pressure  138  mm.  mercury. 


TABLE  210. 
BOILING-POINTS   OF   INORGANIC   COMPOUNDS.4 


213 


Boiling-point. 

£ 

Substance. 

Chemical  Formula. 

Particular 

o 

Date  of 

Min. 

Max 

or  Aver- 

tj 

Publication. 

age  Values. 

^ 

Air  t  

—122 

1884 

TO    ' 

1884 

Aluminum  chloride  J  . 

A1C13 

_ 

_ 

207.5 

3 

1888 

"          nitrate     . 

A1(N08)3+9H20 

- 

- 

134. 

4 

1859 

Ammonia  . 

NH8 

— 

— 

—38-5 

5 

I863 

Antimonietted  hydrogen 

SbH3 

_ 

_ 

-18. 

2 

1886 

Antimony  pentachloride  § 

SbCl5 

IO2. 

103. 

_ 

6 

1889 

"        trichloride 

SbCl8 

216. 

223-5 

220. 

_ 

— 

Bismuth  trichloride   . 

BiCl3 

427. 

447- 

435- 

5>7 

_ 

Cadmium  chloride     . 

CdCl2 

861. 

954- 

908. 

8 

1880 

"         nitrate 

Cd(N03)2+4H20 

- 

132. 

4 

l859 

Calcium  nitrate  . 

Ca(NO8)2+4H2O 

— 

_ 

132. 

4 

Carbon  dioxide  .        . 

C02 

—78.2 

—80. 

—79.1 

1863-1880 

"        disulphide     . 

CS2 

46. 

47-4 

46.1 

_ 

_ 

"        monoxide 

CO 

190. 

—  T93- 

2,  I 

1884 

Chromic  oxychloride 
Chromium  nitrate 

Cr02Cl2 
Cr2(NO3)6+i8H2O 

"5-9 

118. 

117. 
I25-5 

4 

1859 

Copper  nitrate  . 
Cuprous  chloride 

Cu(N03)2+3H20 
Cu2Cl2 

954- 

1032. 

170. 
993- 

8 

1859 
1880 

Hydrobromic  acid  ||    . 

HBr 

— 

—68.1 

9 

1900 

Hydrochloric  acid  ||   . 
Hydrofluoric  acid  ||     . 

HC1 
HF 

: 

- 

-83.1 
—36-7 

9 
9 

1900 
1900 

Hydroiodic  acid 

HI 

_ 

_ 

127. 

10 

1870 

Iron  nitrate 

Fe(N03)8+9H20 

_ 

_ 

125. 

4 

l859 

Magnesium  nitrate    . 

Mg(N03)2+6H20 

- 

_ 

4 

1859 

Manganese  chloride  . 

MnCl2+4H2O 

_ 

_ 

1  06. 

II 

"           nitrate     . 

Mn(NO8)2+6H2O 

_ 

_ 

129.5 

4 

1859 

Mercuric  chloride 

HgCl2 

302. 

307. 

3°4- 

— 

Nickel  nitrate    . 

Ni(NO3)2+6H2O 

_ 

136.7 

4 

1859 

Nitric  acid 

HNO8 

_ 

_ 

86. 

12 

1830 

"      anhydride 

N205 

45- 

50. 

_ 

'3 

1849 

"      oxide 

NO 

_ 

—  T53- 

2 

1885 

Nitrous  anhydride     . 
"        oxide    . 

N208 
N2O 

—  10. 

-87.9 

41 

88.8 

: 

- 

Phosphorus  trichloride 

PC18 

73-8 

76. 

75- 

- 

_ 

"          sesquisulphide 

_ 

380. 

14 

1883 

"          trisulphide 

P2S8 

_ 

_ 

490. 

14 

1886 

"          pentasulphide 

P2S5 

518. 

53°- 

522. 

_ 

"          trioxide 
Silicon  chloride 

P208 
SiCl4 

56.8 

59- 

'£ 

15 

1890 

Sulphuric  acid  . 

I2H2SO4+H2O 

- 

338. 

16 

1853 

Sulphur  trioxide 

SO3 

46. 

47- 

46.3 

— 

"       dioxide 

S02 

—8. 

—10.5 

—9.6 

_ 

_ 

"       chloride 

S2C12 

138. 

144. 

_ 

_ 

Tin,  stannous  chloride 

SnCl2 

656. 

628. 

617! 

- 

_ 

"     stannic          " 

SnC)4 

— 

— 

11  3-9 

17 

1876 

Zinc  chloride     . 

ZnCl2 

676. 

730- 

703- 

_ 

"    nitrate 

Zn(NO8)2+6H2O 

— 

4 

1859 

I  Wroblewski.                      7  Pictet.                                                   13  Deville. 

2  Olszewski.                          8  Carnelley  and  Carleton-  Williams.       14  Isambert. 

3  Friedel  and  Crafts.            9  Ladenburg  and  Kriigel.                       15  Thorpe  and  Tutton. 

4  Ordway.                            10  Topsoe.                                                  16  Marignac. 

5  Regnault.                          n  Clarke,  "  Const,  of  Nature."                17  Thorpe. 

6  Anschiitz  and  Evans.       12  Mitscherlich. 

*  For  a  more  complete  table,  see  Landolt-Bornstein-Meyerhoffer's  Physikalisch-chemische  Tabellen. 
t  Pressure  76  cm.  t  Pressure  2.64  atmos.  §  Pressure  68  mm.  0  Pressure  75.5  cm. 

SMITHSONIAN  TABLES. 


214 


TABLES  211-213.    MELTING-POINTS, 

TABLE  211.  — Melting-point  o!  Mixtures. 


Metals. 

Melting-points,  C°. 

j 

Percentage  of  metal  in  second  column. 

0% 

10% 

20% 

30% 

40% 

50% 

60% 

70% 

80% 

90% 

100% 

Pb.  Sn. 

326 

2QO 

270 

250 

230 

215 

200 

1  80 

190 

210 

232 

I 

Bi. 

322 

29O 

— 

179 

145 

126 

168 

205 

— 

268 

7 

Te. 

322 

710 

790 

880 

917 

760 

600 

480 

410 

425 

446 

8 

Ag. 

328 

460 

545 

590 

620 

650 

70S 

775 

840 

90S 

959 

9 

Na. 

360 

420 

400 

370 

330 

290 

250 

200 

130 

96 

13 

Cu. 

326 

930 

953 

953 

953 

953 

953 

975 

IOIO 

1045 

1081 

2 

Sb. 

326 

250 

275 

330 

395 

440 

490 

525 

560 

600 

632 

16 

Al.  Sb. 

650 

750 

840 

925 

945 

950 

970 

IOOO 

1040 

IOIO 

632 

i? 

Cu. 

650 

630 

600 

56o 

540 

580 

610 

755 

930 

1055 

1084 

18 

Au. 

655 

675 

740 

800 

855 

915 

970 

1025 

1055 

675 

1062 

10 

Ag. 

650 

625 

6iS 

600 

590 

58o 

575 

570 

650 

750 

954 

i? 

Zn. 

654 

640 

620 

600 

580 

560 

530 

5io 

475 

425 

419 

ii 

Fe. 

654 

635 

630 

1125 

1170 

1  200 

1350 

1450 

1520 

1570 

1600 

3 

Sn. 

650 

645 

635 

625 

620 

605 

590 

570 

560 

540 

232 

17 

Sb.  Bi. 

632 

610 

590 

575 

555 

540 

520 

470 

405 

330 

268 

10 

Ag. 

630 

595 

570 

545 

520 

500 

505 

545 

680 

850 

959 

9 

Sn. 

622 

600 

570 

525 

480 

430 

395 

350 

310 

255 

232 

19 

Zn. 

632 

555 

Sio 

540 

570 

565 

540 

525 

Sio 

470 

419 

17 

Ni.  Sn. 

1455 

1380 

1290 

1  200 

1235 

1290 

1305 

1230 

1060 

800 

232 

17 

Na.  Bi. 

96 

425 

520 

590 

645 

690 

720 

730 

715 

570 

268 

13 

Cd. 

96 

125 

185 

245 

285 

325 

330 

340 

360 

390 

322 

13 

Cd.  Ag. 

322 

420 

520 

610 

700 

760 

805 

850 

895 

940 

954 

17 

Tl. 

321 

300 

285 

270 

262 

258 

245 

230 

210 

235 

302 

14 

Zn. 

322 

280 

270 

295 

313 

327 

340 

355 

370 

390 

419 

II 

Au.  Cu. 

1063 

940 

910 

925 

943 

968 

993 

1018 

I04O 

1060 

1083 

4 

Ag. 

1064 

1062 

1061 

1058 

1054 

1049 

1039 

1025 

1006 

982 

963 

5 

Pt. 

1075 

1125 

1190 

1250 

1320 

1380 

1455 

1530 

1610 

1685 

1775 

20 

K.  Na. 

62 

17-5 

—  10 

—3-5 

5 

ii 

26 

4i 

58 

77 

97-5 

15 

Hg. 

_ 

— 

90 

no 

135 

162 

265 

— 

13 

Tl 

62.5 

133 

165 

188 

205 

215 

220 

240 

280 

305 

301 

14 

Cu.  Ni. 

I080 

1180 

1240 

1290 

1320 

1335 

1380 

1410 

1430 

1440 

1455 

17 

Ag. 

1082 

1035 

990 

945 

910 

870 

830 

788 

814 

875 

960 

9 

Sn. 

1084 

1005 

890 

755 

725 

680 

630 

580 

530 

440 

232 

12 

Zn. 

1084 

1055 

IOOO 

945 

890 

870 

840 

785 

700 

570 

419 

6 

Ag.  Zn. 

959 

850 

755 

70S 

690 

660 

630 

610 

570 

SOS 

419 

II 

Sn. 

959 

870 

750 

630 

550 

495 

450 

420 

375 

300 

232 

9 

Na.  Hg. 

96.5 

90 

80 

70 

60 

45 

22 

55 

95 

215 

13 

1  Roberts-Austen,  Engineering,  63,  223,  1897. 

2  j       Rap.  Cong.  Phys.  Paris,  1900. 

3  "  Engineering,  59,  744,  1895. 

4  "  Proc.  Roy.  Soc.  67,  105,  1900. 

5  "  Chem.  News,  87,  2,  1903. 

6  "  Engineering,  12/2,  221,  1897. 

7  Kapp,  Diss.,  Konigsberg,  1901. 

8  Fay  and  Gilson,  Trans.  Am.  Inst.  Min.  Eng.  Nov. 

1901. 

9  Heycock  and  Neville,  Phil.  Trans.  i89A,  1897. 
IO         "  "         "          "          "    I94A,  201, 1900. 


11  Heycock  and  Neville,  J.  Chem.  Soc.  71,  1897. 

12  Phil.  Trans.  202A,  i,  1903. 

13  Kurnakow,  Z.  Anorg.  Chem.  23,  439,  1900. 

14  "         30,  86,  1902. 
15 

16  Roland-Gosselin,  Bui.  Soc.  d'l 

17  Gautier,  "         (5) 

18  Le  Chatelier,  ••        (4)  JO,  573, 

1895. 

19  Reinders,  Z.  Anorg.  Chem.  25,  113,  1896. 

20  Erhard  and  Schertel,  Jahrb.  Berg  -u.  Hiittenw. 

Sachsen.  1879,  17. 


30,  109,  1902. 
'Encour.  (5)  i,  1896. 


TABLE  212.  — Alloy  of  Lead,  Tin,  and  Bismuth. 


Per  cent. 

Lead    .... 
Tin  

32.0 
iS-5 
52.5 

25.8 
19.8 

54-4 

25.0 
15.0 
60.0 

43-0 
14.0 
43.0 

33-3 
33-3 
33,3 

10.7 
23.1 
66.2 

50.0 
33-0 
17.0 

35-8 
52.1 
12.  1 

20.0 
6O.O 
20.0 

70.9 

9.1 

2O.O 

Bismuth  .     .     . 

Solidification  at 

96° 

101° 

125° 

128° 

145° 

148° 

161° 

181° 

182° 

234° 

Charpy,  Soc.  d'Encours,  Paris,  1901. 


TABLE  213.  — Low  Melting-point  Alloy. 


•Percent. 

Cadmium  .  . 
Tin  .  .  .  . 
Lead  .... 
Bismuth  .  .  . 

10.8 
14.2 
24-9 
50.1 

IO.2 
14-3 
25-1 
50.4 

I4.8 

7.0 
26.0 
52.2 

I3-I 
13-8 
24-3 
48.8 

6.2 

9.4 
34-4 
SO.o 

7-1 

39-7 
53.2 

6.7 

434 
49-9 

Solidification  at 

65.5° 

67.5° 

68.5° 

68.5° 

76.5° 

89.5° 

95° 

Drewitz,  Diss.  Rostock,  1902. 

All  compiled  from  Landolt-Bornstein-Meyerhoffer's  Physikalisch-chemische  Tabellen. 
SMITHSONIAN  TABLES. 


TABLE  214.  215 

DENSITIES,    MELTING-POINTS,    AND    BOILING-POINTS    OF    SOME 
ORGANIC  COMPOUNDS. 

N.B.  —  The  data  in  this  table  refer  only  to  normal  compounds. 


Substance. 

Formula 

Temp. 

Den- 
sity. 

Melting- 
point. 

Boiling-point. 

Authority. 

(a)  Paraffin  Series  :  CnH2rt+2. 

Methane* 
Ethanet 
Propane 

CH4 
C2H6 
C8H8 

-164. 

0 
0 

0.415 
.446 
.536 

—171.4 

-165. 
—93- 
—45- 

Olszewski,  Young. 
Ladenburg,     " 
Young,  Hainlen. 

Butane 

C4Hio 

0 

.00 

— 

Butlerow,  Young. 

Pentane 
Hexane 

C'HH 

o 

17- 

.663 

- 

§3 

Thorpe,  Young. 
Schorlemmer. 

Heptane 

C7H16 

0 

.701 

- 

4 

Thorpe,  Young. 

Octane 

C8His 

o 

.719 

— 

I25-5 

«             « 

Nonane 

CgH2o 

o 

•733 

—SI- 

150. 

Krafft. 

Decane 

CioH22 

0 

•745 

—  31' 

« 

Undecane 

CUH24 

0 

-26. 

195. 

M 

Dodecane 

Ci2H26 

o 

•765 

—  12. 

214. 

ft 

Tridecane 

Ci8H28 

o 

.771 

—6. 

234. 

u 

Tetradecane 

Ci4H8o 

4- 

•775 

5. 

252. 

ft 

Pentadecane 

Ci5H82 

10. 

.776 

IO. 

270. 

« 

Hexadecane 

CieH84 

18. 

•775 

1  8. 

287. 

M 

Heptadecane 

C17H86 

22. 

•777 

22. 

3°3- 

M 

Octadecane 

CisH88 

28. 

•777 

28. 

3J7' 

M 

Nonadecane 

Ci9H4o 

32- 

•777 

32- 

33°- 

M 

Eicosane  .     . 

C-joH^ 

37- 

.778 

37- 

I2I.§ 

M 

Heneicosane 

C2iH44 

40. 

.778 

40. 

i29.§ 

M 

Docosane     . 

C22H46 

44. 

.778 

44- 

« 

Tricosane    . 

C2gH48 

48. 

•779 

48. 

J42-5§ 

« 

Tetracosane 
Heptacosane 

C24H-5o 
C27HS6 

•779 
.780 

£ 

2434 

I72.§ 

U 

Pentriacontane 

C8iri64 

68.' 

.781 

68. 

ft 

Dicetyl    .     .     . 

C82Hgg 

70. 

.781 

70. 

205.§ 

u 

Penta-tria-contane 

C85H72 

75- 

.782 

75- 

u 

(b)  Olefines,  or  the  Ethylene  Series  »  CwHaw. 

Ethylene 

C2H4 

_ 

0.610 

-169. 

—103. 

Wroblewski  or  Olszewski. 

Propylene 
Butylene  . 

C3H6 
C4H8 

—13-5 

•635 

—50.2 

I. 

Ladenburg,  Kriigel. 
Sieben. 

Amylone 
Hexylene 

C6H10 

0 

.76 

: 

36. 

69. 

Wagner  or  Saytzeff. 
Wreden  or  Znatowicz. 

Heptylene 

cJnS 

19-5 

•703 

_ 

Morgan  or  Schorlemmer. 

Octylene  . 
Nonylene 

cjni; 

17- 

20. 

.722 
.767 

— 

122.-I23. 

I40.-I42. 

Mb'slinger. 
Beilstein,  "  Org.  Chem." 

Decylene 

CioH2o 

— 

— 

. 

175. 

«                    4<                 it 

Undecylene 

CnH22 

20. 

•773 

~ 

I96.-I97. 

«           «         « 

Dodecylene 

Ci2H24 

—  31- 

•795 

—  31- 

2I2.-2I4. 

««               ft            ft 

Tridecylene 

CisH2g 

•774 

233- 

Bernthsen. 

Tetradecylene 

Ci4H28 

—  12. 

•794 

—  12. 

127-t 

Krafft. 

Pentadecylene 

CisH8o 

— 

.814 

— 

247. 

Bernthsen. 

Hexadecylene 
Octadecylene 

Ci6H32 
Ci8H86 

18.' 

•792 
.791 

iS. 

155.1 

179-t 

Krafft,  Mendelejeff,  etc. 
Krafft. 

Eicosylene  . 

C^H^ 

o 

.871 

- 

390.-400. 

Beilstein,  "  Org.  Chem." 

Cerotene 

C27Hs4 

— 

— 

58. 

Bernthsen. 

Melene    .    . 

C80H60 

62. 

• 

*  Liquid  at—  n.°  C.  and  180  atmospheres'  pressure  (Cailletet). 

"  +  4.°  "     "    46  "  «» 

i  Boiling-point  under  15  mm.  pressure. 
§  In  vacuo. 


SMITHSONIAN  TABLES. 


2l6  TABLE   214  (continued}. 

DENSITIES,   MELTING-POINTS,   AND   BOILING-POINTS   OF  SOME 
ORGANIC   COMPOUNDS. 


Substance. 

Chemical 
formula. 

Temp. 

Specific 
gravity. 

Melting- 
point. 

Boiling- 
point. 

Authority. 

(C)  Acetylene  Series  :  CnH2ft__2. 

Acetylene  

C2H2 

—  81. 

g 

Villard. 

Allylene      

C3H4 

_ 

_ 

_ 

Ethylacetylene    .    .     . 

C4H6 

- 

- 

- 

-j-  18. 

Bruylants,  Kutsche- 

roff,  and  others. 

Propylacetylene  .    .    . 
Butylacetylene     .     .     . 

C6H8 

: 

— 

- 

48-50. 

68-70. 

Bruylants,  Taworski. 
Taworski. 

Oenanthylidene  .    .    . 

C7Hi2 

- 

- 

- 

IOO.-IOI. 

Beilstein,    and    oth- 

ers. 

Caprylidene    .... 

C8H14 

0. 

0.771 

_ 

133.-!  34. 

Behal. 

Undecylidene  .    .    .     . 

- 

- 

2IO.-2I5- 

Bruylants. 

Dodecylidene      .     .    . 

Ci2H22 

—  9' 

.810 

—  9- 

105.* 

Krafft. 

Tetradecylidene  .     .     . 
Hexadecylidene  .     .     . 

Ci4H26 

+6.5 

20. 

.806 
.804 

+  6.5 
20. 

I  DO* 

« 

Octadecylidene   .    .    . 

Ci8H34 

30- 

.802 

30- 

184.* 

" 

(d)  Monatomic  alcohols  :  CWH2W+IOH. 

Methyl  alcohol 

CH3OH 

O. 

0.8  1  2 

_ 

66. 

Ethyl  alcohol  . 

C2H5OH 

0. 

.806 

—  130.1 

78. 

Propyl  alcohol 

C8H7OH 

o. 

.817 

— 

97- 

From  Zander,  "  Lieb. 

Butyl  alcohol  . 

C4H9OH 

o. 

.823 

_ 

117. 

Ann."  vol.  224,  p.  85, 

Amyl  alcohol  . 

C6HnOH 

0. 

.829 

- 

138- 

and  Krafft,  "Ber." 

Hexyl  alcohol 

C6Hi3OH 

0. 

.833 

— 

vol.  16,  1714, 

Heptyl  alcohol 

C7Hi5OH 

0. 

.836 

— 

\76. 

1     19,  2221, 

Octyl  alcohol  . 

C8H17OH 

0. 

•839 

- 

!95- 

Nonyl  alcohol 

C9Hi9OH 

0. 

.842 

—  5- 

213. 

and  also  Wroblew- 

Decyl  alcohol 

CioH2iOH 

+  7- 

•839 

+  7- 

231. 

ski  and  Olszewski, 

Dodecyl  alcohol 

C12H25OH 

24. 

.831 

I43-* 

"  Monatshefte," 

Tetradecyl  alcohol 

C14H29OH 

38. 

.824 

38. 

167.* 

vol.  4,  p.  338. 

Hexadecyl  alcohol 

C16H33OH 

.818 

50. 

190.* 

Octadecyl  alcohol 

C18H37OH 

59- 

.813 

59- 

211.* 

(e)  Alcoholic  ethers  :  CnU2ft+2O. 

Dimethyl  ether  .    .    . 

C2H6O 

_ 

_ 

- 

-23.6 

Erlenmeyer,  Kreich- 

baumer. 

Diethyl  ether  .     . 

C4H100 

4- 

0.731 

—  117 

+  34-6 

Regnault,  Olszewski. 

Dipropyl  ether    . 

C6H140 

0. 

.763 

90.7 

Zander  and  others. 

Di-iso-propyl  ether 

C6H140 

0. 

•743 

— 

69. 

" 

Di-n-butyl  ether  . 

C8H180 

o. 

.784 

- 

141. 

Lieben,  Rossi,  and 

others. 

Di-sec-butyl  ether 

C8H180 

21. 

.756 

- 

121. 

Kessel. 

Di-iso-butyl     " 

C8H180 

1C. 

.762 

— 

122. 

Reboul. 

Di-iso-amyl      " 
Di-sec-hexyl    " 

CioH22O 
Ci2H260 

0. 

•799 

_ 

1  70.-!  7  5. 

2O3.-2OO. 

Wurtz. 
Erlenmeyer  and 

Wanklyn. 

Di-norm-octyl  "       .     . 

Ci6H340 

17- 

.805 

- 

280.-282. 

Moslinger. 

(f)  Ethyl  ethers  :  CnH2n+2O. 

Ethyl-methyl  ether  .     . 
"     propyl      "      .     . 

C3H80 
C6H120 

o. 

20. 

0.725 
0-739 

- 

II. 

Wurtz,  Williamson. 
Chancel,  Bruhl. 

"     iso-propyl  ether  . 

C6H120 

0. 

•745 

— 

54- 

M  arko  wn  iko  w. 

"     norm-butyl  ether 

C6H140 

0. 

.769 

— 

92. 

Lieben,  Rossi. 

"     iso-butyl  ether     . 
"     iso-amyl  ether 

C6H140 
C7H160 

.1 

.764 

- 

78.-8o. 

112. 

Wurtz. 
Williamson  and 
others. 

"    norm-hexyl  ether 

C8H180 

- 

- 

- 

I34--I37- 

Lieben,  Janeczek. 

"    norm-heptyl  ether 
"    norm-octyl  ether 

C9H20O 
CioH22O 

16. 
17- 

.790 
•794 

- 

i826i8 

Cross. 
Moslinger. 

*  Boiling-point  under  15  mm.  pressure. 

t  Liquid  at  —  n.°  C.  and  180  atmospheres'  pressure  (Cailletet). 


SMITHSONIAN  TABLES. 


TABLE  21 5.  2 1/ 

LOWERING  OF  FREEZING-POINTS  BY  SALTS  IN  SOLUTION. 

In  the  first  column  is  given  the  number  of  gramme-molecules  (anhydrous)  dissolved  in  1000 
grammes  of  water;  the  second  contains  the  molecular  lowering  of  the  freezing-point ;  the  freez- 
ing-point is  therefore  the  product  of  these  two  columns.  After  the  chemical  formula  is  given 
the  molecular  weight,  then  a  reference  number. 


g.  mol.              1'g 
looo  g.  HjO          *3  | 

g.  mol. 
looo  g.  H2O 

|| 

looo  g.  H2O           "3  | 
MM 

g.  mol. 
looo  g.  H2O 

Molecular  1 
Lowering.  1 

Pb(N03)2,  331.0:  1,2. 

0.0500 

347° 

0.4978                  2.02° 

MgCl2,  95.26  :  6, 

14* 

0.000362             5.5° 

.IOOO 

342 

.8lI2                 2.01 

O.OIOO 

5-lQ 

.OOI2O4             5.30 

.2000 

3-32 

1.5233                 2.28 

.0500 

4.98 

.002805             5.17 

.500 

3-26 

Bad,,  208.3:  3,6,  13. 

.1500 

4.96 

.005570          4-97 

I.OOO 

3-14 

o".OO2OO               5.5° 

.3000 

5.186 

.01737            4.69 

LiNO3,  69.07  :  9. 

.00498               5.2 

.6099 

5-69 

.5015              2.99 

0.0398 

34° 

.0100             5.0 

KC1,  74.60:  9,  17-19. 

Ba(N03)2,  261.5:  i. 

.1671 

3-35 

.0200                  4.95 

0.02910 

3-54° 

0.000383           5.6° 

.4728 

3-35 

.04805                4.80 

.05845 

3-46 

.001259           5.28 

1.0164 

3-49 

.100              4.69 

.112 

3-43 

.002681            5.23 

A12(SO4)S,  342.4  : 

10. 

.200                     4.66 

.3139 

.005422           5.13 
.008352           5.04 

0.0131 
.0261 

5.6° 

4-9 

.500                     4.82 
.586                     5.03 

I.OOO 

3:286 

Cd(N03)2,  236.5:  3. 

•0543 

4-5 

.750                     5.21 

1.989 

3-25 

0.00298              5.4° 
.00689              5-25 
.01997              5.18 

•04873           5-!5 

.1086                4.03 
•2!7                       3-83 
CdSO4,  208.5:  i,  ii. 
0.000704            3.35° 

CdCl2,  183.3:  3,14- 
0.00299                5.0° 
.00690               4.8 
.O2OO                  4.64 

3-269         3.25 

NaCl,  58.50:  3,  20,  12,  16. 
0.00399           3.7° 

.01000         3.67 

AgNO3,  167.0:  4,  5. 
0.1506                 3.32° 

.002685 
•OH5I 

3-05 
2.69 

.0541                   4.  1  1 
.O8l8                  3.93 

.O22I 
.04949 

3-55 
3-51 

.5001                 2.96 

.03120 

2.42 

.214                     3.39 

.I08I 

348 

.8645                 2.87 

•H73 

2.13 

.429                     3.03 

.2325 

342 

1.749                   2.27 

.4129 

.  _/r 

.858                     2.71 

4293 

3-37 

2-953                   I-8S 
3.856                   1.64 
0.0560                 3.82 
.1401                 3.58 
.3490                 3.28 
KNO3,  101.9:  6,  7. 
o.oioo             3.5 

-7501 
!-253 

K2S04,  174.4:  3.  5, 
O.OO2OO 
.00398 
.00865 
.0200 

1.76 
1.86 

6,  10,  12. 

5-4° 
5-3 
4.9 
4.76 

1.072                     2.75 

CuCl2,  134.5  :  9. 
0.0350              4.9° 
.1337               4.81 
.3380              4-92 
.7149               5-32 

.700 

NH4C1,  53-52:  6, 
O.OIOO 
.0200 

•0350 
.IOOO 

343 

'H 

3-56 
3-50 
3-43 

.0200                   3.5 
.0500                   3.41 
.IOO                      3.31 

.0500 
.IOOO 
.200 

4.60 

4-32 
4.07 

CoCl2,  129.9  :  9- 
0.0276               5.0° 
.1094              4-9 

.2000 

.4000 
.7000 

3-393 
34i 

.200                      3.19 

454 

3-87 

.2369               5.03 

LiCl,  42.48  :  9,  15 

.250                      3.08 

CuSO4,  159.7:  1,4,  ii. 

4399             5-3° 

0.00992 

3-7° 

0.000286 

3-3° 

•538               5-5 

.°455 

3-5 

.750               2.81 

.000843 

3-15 

CaCI2,  m.o:  5,  13-16. 

.09952 

3-53 

i.ooo               2.66 

.002279 

3-°3 

o.oioo              5.1° 

.2474 

3-5° 

NaN03,  85.09  :  2,  6,  7. 
o.oioo              3.6° 
.0250              3.46 

.006670 
.01463 
.1051 

2.79 

1:11 

.05028            4.85 
.1006              4.79 
.5077              5-33 

.5012 
•7939 
BaBr2,  297.3  :  14. 

3.7i 

f  »O 

.0500              3.44 

.2074 

1.95 

.946               M 

O.IOO 

.2000                   3-345 

4043 

1.84 

2.432               8.2 

.150 

4-9 

.500             3.24 

.8898 

1.76 

3469             1  1-5 

.200 

5.00 

•5OI5             3.30 

MgSO4,  120.4:  i, 

4,  n. 

3.829             14.4 

.500 

5.18 

i.ooo                3.15 

0.000675 

3.29 

0.0478             5.2 

AlBr,,  267.0:  9. 

1.0030           3.03 

.002381 

3.10 

•153               4-91 

0.0078 

1.4° 

NH4N08,  80.11  :  6,  8. 

.01263 

2.72 

•331               5.15 

•0559 

1.2 

o.oioo             3.6° 
.0250           3.50 

.0580 
.2104 

2.65 
2.23 

.612               5.47 
.998               6.34 

.1971 
4355 

1.07 
1.07 

i  Hausrath,  Ann.  Phys.  9,  1902. 
2  Leblanc-Noyes,  Z.  Phys.  Ch.  6,  1890. 
3   Tones,  Z.  Phys.  Ch.  ii,  1893. 
4  Raoult,  Z.  Phys.  Ch.  2,  1888. 

ii  Kahlenberg,  J.  Phys.  Ch.  5,  1901. 
12  Abegg,  Z.  Phys.  Ch.  20,  1896. 
13  Jones-Getman,  Am.  Ch.  J.  27,  1902. 
14  Jones-Chambers,  Am.  Ch.  J.  23,  1900. 

S  Arrhenius,  Z.  Phys.  Ch.  2,  1888. 
6  Loomis,  Wied.  Ann.  57,  1896. 

15  Loomis,  Wied.  Ann.  60,  1897. 
1  6  Roozeboom,  Z.  Phys.  Ch.  4,  1889. 

7  Tones,  Am.  Chem.  J.  27,  1902.                                                17  Raoult,  Z.  Phys.  Ch.  27,  1898. 
8  Jones-Caldwell,  Am.  Chem.  J.  5,  1901.                                  18  Roloff,  Z.  Phys.  Ch.  18,  1895. 
9  Biltz,  Z.  Phys.  Ch.  40,  1902.                                                    19  Kistiakowsky,  Z.  Phys.  Ch.  6,  1890, 
10  Jones-Mackay,  Am.  Chem.  J.  19,  1897.                                 20  Loomis,  Wied.  Ann.  51,  1894. 
Compiled  from  Landolt-Bornstein-Meyerhofier's  Physikalisch-chemische  Tabellen. 

SMITHSONIAN  TABLES. 

21 8  TABLE  21 5  (continued). 

LOWERING   OF   FREEZING-POINTS    BY   SALTS    IN   SOLUTION  (continued). 


g.  mol. 
looo  g.  H2O 

Molecular  1 
Lowering.  1 

g.  mol. 

Molecular  1 
Lowering.  1 

g.  mol. 
1000  g.  H2O 

Molecular  1 
Lowering.  1 

g.  mol. 
1000  g.  H2O 

Molecular  1 
Lowering.  1 

1000  g.  H2O 

CdBr2,  272.3  :  3,  14. 

KOH,  56.16:  1,15,23. 

Na2SiO3,  122.5  :  * 

0.472 

2.20° 

0.00324 

5-1 

0.00352 

3.60 

0.01052 

6.4° 

•944 

2.27 

.00718 

4.6 

.00770 

3-59 

.05239 

5-86 

1.620 

2.60 

.03627 
.0719 

3-84 

3-39 

.02002 
.05006 

3-44 
343 

.1048 
.2099 

5.28 
4.66 

(COOH)2,  90.02  : 

O.OIOO2 

3-3° 

.1122 

3.18 

.lobi 

3-42 

•5233 

3-99 

.O2OO5 

3.19 

'      .220 
.440 

2.96 
2.76 

.2003 

3-424 
3-50 

HC1,  36.46  : 
i-3,  6,  13,  18,  22. 

.05019 
.IOO6 

•3-03 
2.83 

.800 

2-59 

.465 

3-57 

0.00305 

3'2f 

.2O22 

—  "J 

2.64 

CuBr,,  223.5  :  9. 

CH3OH,  33.03  :  24,  25. 

.00695 

3.66 

.366 

2.56 

0.0242 

C  T  *"* 

O.OIOO 

I.o 

.OIOO 

3-6 

.648 

2.1 

.0817              5.1 
.2255              5.27 
.6003              5.89 
CaBr,,  200.0:  14. 
0.0871                5.1° 
.1742                5.18 
.3484                5.30 
.5226                5.64 
MgBn,,  184.28  :  14. 
0.0517               5.4° 
.103                 5.16 
.207                 5.26 

.0301 
.2018 

1.046 
341 

6.200 
C2H6OH,  46.04: 

I,  12,  17 
O.OOO4O2 
.004993 

.0100 

.02892 

.0705 

.1292 

1.82 

1.811 
1.86 
1.88 
1.944 

1.81 

1.707 
1.85 
1.829 

.01703 
.0500 
.1025 
.2000 
.3000 
.464 
.516 
1.003 
1.032 
1.500 
2.000 
2.II5 
3-000 

3-59 
3-59 
3-56 
3-57 
3.612 
3-68 
3-79 
3-95 
4.10 
4.42 
4-97 
4.52 
6.03 

C3H5(OH)3,  93.06 
O.O2OO 
.1008 
.2031 

•535 
2.40 

5-24 

(C2H6)20,  74.08: 
O.OIOO 
.0201 
.1011 
.2038 

3 

s® 

1.86 
1.85 
1.91 
1.98 
2.13 

lie; 

1.72 
1.702 

•5I7 

KBr,  119.1:  9,  21. 
0.0305 
.1850 
.6801 
.250 

>":> 

3-6l° 

3-49 
3-30 
3-78 

.2024 

•5252 

1.0891 

1.760 
3.901 
7.91 

1.832 
1.834 
1.826 

1-83 
1.92 

2.02 

3-053                    4.90 
4.065                    5.67 
4.657                    6.19 

HNO3,  63.05  :  3,  13,  15. 

0.02004            3.55° 
•05015            3-50 

Dextrose,  180.1: 
0.0198 
.0470 
.1326 
.4076 
I.IO2 

14.  30. 
1.84° 
1.85 
1.87 
1.894 
1.921 

.500 

3-3° 

II.  II 

2.12 

.0510 

3.71 

Levulose,  180.1  : 

*4t  *5- 

Cdl,,  366.1  :  3,  5,  22. 

18.76 

I  8l 

.1004 

3-48 

O.O2OI 

I.87° 

0.00210 

X-       x- 

4-5" 

0.0173 

1.80 

.1059 

3-53 

.2050 

1.871 

.00626 

4.0 

.0778 

1.79 

.2015 

345 

•554 

2.01 

.O2O62 
.04857 

3-52 
2.70 

K2C03,  138.30:6. 
O.OIOO 

.250 
.500 

3-50 
3.62 

1.384 
2-77 

2.32 
3-04 

.1360 

2-35 

.0200 

4-93 

I.OOO 

3-8o 

CHO,  342.2  :  i,  24 

,26. 

2.13 

.0500 

4.71 

2.000 

4.17 

0.000332 

I.900 

2.23 

.100 

4-54 

3.000 

4.64 

.001410 

1.87 

2.51 

.200 

4-39 

HSP02,  66.0:  29. 

.009978 

1.86 

KI,  166.0  :  9,  2. 

Na2COH,  I06.ZO  :  6. 

0.1260 

2.90° 

.O2OI 

1.88 

0.0651 

3-5° 

O.OIOO 

5-T° 

.2542 

2-75 

•I3°5 

1.88 

.2782 
.6030 
1.003 

3-50 
3-42 
3-37 

.0200 
.0500 
.IOOO 

4-93 
4.64 

4.42 

•5171 
1.071 
HPO,  820:  4,5. 

2-59 
245 

H2S04,  98.08  : 
131*0,31-33. 
0.00461           4.8° 

SrI2,  341.3:  22. 

.2000 

4.17 

0.0745 

3-0° 

.0100 

449 

0.054 

5«* 

Na,SO3,  126.2  :  28 

.1241 

2.8 

.0200 

4-32 

.108 

5-2 

"0.1044 

4-51° 

.2482 

2.6 

.0461 

4.10 

.216 
.327 

5-35 
5-52 

•3397 
.7080 

3-74 
3-38 

i.oo               2.39 
H3PO4,  98.0  :  6,  22. 

.100 

.200 

3.96 

3-85 

NaOH,  40.06:  15. 

Na2HPO4,  142.1  : 

22,  29. 

O.OIOO 

2.8° 

.400 

3.98 

O.O2OO2 

345° 

O.OIOOI 

5-o° 

.0200 

2.68 

1.  000 

4.19 

.05005 
.1001 

3-45 
34i 

.02003 
.05008 

4.84 
4.60 

.0500 

.1000 

249 
2.36 

1.500 

2.OOO 

4.96 
5.65 

.2000 

3407 

.IOO2 

4-34 

.2000 

2.25 

2.500 

6-53 

1-20  See 
21 

22  Chambers-Frazer,  Am.  Ch.  J.  23,  1900. 

23  Noyes- Whitney,  Z.  Phys.  Ch.  15,  1894. 

24  Loomis,  Z.  Phys.  Ch.  32,  1900. 

25  Abegg,  Z.  Phys.  Ch.  15,  1894. 

26  Nernst-Abegg,  Z.  Phys.  Ch.  15,  1894. 

SMITHSONIAN  TABLES. 


10  bee  page  217. 
Sherrill,  Z.  Phys.  Ch.  43,  1903. 
22  Chambers-Frazer,  Am.  Ch.  J.  23,  it 
ITS.  Ch.  15,  iS 


3 


Pictet-Altschul,  Z.  Phys.  Ch.  16,  1895. 
Earth,  Z.  Phys.  Ch.  9,  1892. 

29  Petersen,  Z.  Phys.  Ch.  ir,  1893. 

30  Roth,  Z.  Phys.  Ch.  43.  1003. 

31  Wildermann,  Z.  Phys.  Ch.  15,  1894. 

32  Jones-Carroll,  Am.  Ch.  J.  28,  1902. 

33  Jones-Murray,  Am.  Ch.  J.  30,  1903. 


TABLE  216.  219 

RISE   OF   BOILING-POINT  PRODUCED  BY  SALTS  DISSOLVED  IN  WATER.* 

This  table  gives  the  number  of  grammes  of  the  salt  which,  when  dissolved  in  100  grammes  of  water,  will  raise  the 
boiling-point  by  the  amount  stated  in  the  headings  of  the  different  columns.    The  pressure  is  supposed  to  be  76 

centimetres. 


Salt. 

re. 

2° 

3° 

4° 

6° 

7°        10° 

16° 

20° 

25 

BaCl2  +  2H20    . 

15.0 

3I.I 

47-3 

63-5 

(71-6  g 

1 
ves  4°.  5  rise 

of  temp 

.) 

CaCl2 
Ca(NO3)2  4-  2H2O     . 

6.0 

I2.O 

11.5 

25-5 

16.5 
39-5 

2I.O 

53-5 

68^5 

32.0 
IOI.O 

41-5 
152.5 

55-5 
240.0 

69.0 
331-5 

84.5 
443-5 

KOH           ... 

KC2H3O2    . 

fi 

9-3 

12.0 

I  7.6 

1  8.0 

17.4 

24-5 

20.5 
31.0 

26.4 

44.0 

34-5 
63-5 

47-o 
98.0 

57-5 
134.0 

3 

KC1     . 

9.2 

I6.7 

23-4 

29.9 

36-2 

48.4 

(57.4  gives  a  rise  of  8°.  5) 

K2CO3 

"•5 

22.5 

32.0 

40.0 

47-5 

60.5 

78.5 

'03-5 

127-5 

152-5 

KC1O3 

13.2 

27.8 

44.6 

62.2 

KI       .        . 
KN03 

15.0 
15.2 

3O.O 
31.0 

45-0 
47-5 

60.0 
64.5 

74-0 
82.0 

99-5 
120.5 

134- 

188.5 

185.0 
338.5 

(22Ogi\ 

es  i8°.5) 

K2C4H406+iH20    . 

18.0 

36.0 

54-o 

72.0 

90.0 

126.5 

182.0 

284.0 

KNaC4H4O6       . 
KNaC4H406  +  4H20 

17-3 
25.0 

34-5 
53-5 

84.0 

68.1 
118.0 

84.8 

119.0 
266.0 

171.0 

554-0 

272.5 
55IO-o 

390.0 

510.0 

LiCl    .... 

3-5 

7.0 

1  0.0 

12.5 

15.0 

20.0 

26.0 

35-o 

42.  5 

50.0 

LiCl  +  2H2O      . 

6.5 

13.0 

19-5 

26.0 

32-0 

44-0 

62.0 

92.0 

123.6 

160.5 

M|s04  +  7H20' 

1  1.0 

4i.5 

22.O 
87.5 

1382 

44-0 
196.0 

55-o 
262.0 

77-0 

II  0.0 

170.0 

241.0 

334-5 

NaOH 

4-3 

8.0 

M-3 

14-3 

17.0 

22.4 

30.0 

41.0 

51.0 

60.1 

NaCl  .... 

6.6 

12.4 

17.2 

21.5 

25-5 

33-5 

(40.7  gives  8°.8 

rise) 

NaNO3        . 

9.0 

18.5 

28.0 

38.0 

48.0 

68.0 

99-5 

156.0 

222.O 

NaC2H3O2  4-  3H2O  . 

14.9 

30.0 

46.1 

62.5 

79-7 

118.1 

194.0 

480.0 

6250.0 

Na2S2O3      . 
Na2HPO4  . 

14.0 
17.2 

27.0 
34-4 

39-o 
51.4 

49-5 
68.4 

59-o 
85-3 

77.0 

104.0 

152.0 

214.5 

311.0 

Na2C4H406  +  2H20  . 
Na2S2O3  +  5H2O 

21.4 
23-8 

44.4 
50.0 

68.2 
78.6 

121.3 
139-3 

183.0 
216.0 

(237-3  gives  8 
400.0  1  1765.0 

°4  rise) 

Na2CO3  4-  ioH2O      . 

34-1 

86.7 

177.6 

369-4 

1052.9 

Na2B4O7  4-  ioH2O     . 
NH4C1 

39- 
6.5 

93-2 

12.8 

254.2 
19.0 

24.7 

(5555-5  gives  4°-5  rise) 
29.7     39.6     56.2       88.5 

NH4NO3    . 

1  0.0 

20.0 

30.0 

41.0 

52.0 

74-o 

108.0 

172.0 

248.0 

337-0 

NH4S04     . 

15.4 

3O.I 

44-2 

58.0 

71.8 

99.1 

(115.3  gives 

108.2) 

SrCl2  +  6H2O    . 

2O.O 

4O.O 

60.0 

81.0 

103.0 

150.0 

234.0 

524.0 

Sr(N08)2     . 

24.0 

45-o 

63.6 

81.4 

97.6 

C4H606       . 

17.0 

34-4 

52.0 

70.0 

87.0 

123.0 

177.0 

272.0 

374-0 

484.0 

C2H204  4-  2H2O 

I9.O 

40.0 

62.0 

86.0 

1  1  2.0 

169.0 

262.0 

540.0 

1316.0 

50000.0 

C6H8O7  4-  H2O 

29.0 

58.0 

87.0 

1  1  6.0 

145.0 

208.0 

320.0 

553-o 

952.0 

Salt.                    40°        60° 

80° 

100° 

120° 

140° 

160°       180° 

200°      240° 

CaCl2  .        .        .    137.5     222.0 

314.0 

KOH   .        .        .      92.5      121.7 
NaOH          .        .93.5     150.8 

152.6 

230.0 

185.0 
345-Q 

219.8 
526.3 

263.1 
800.0 

312.5     375-0 
1333-0  2353.0 

444.4    623.0 
6452.0 

NH4NO3      .        .    682.0    1370.0 
C4H6()6        .        .    980.0   3774.0 

2400.0   4099.0   8547.0 
[infinity  gives  170) 

GO 

1             | 

*  Compiled  from  a  paper  by  Gerlach,  "  Zeit.  f.  Anal.  Chem."  vol.  26. 
SMITHSONIAN  TABLES. 


220 


TABLE  217. 
FREEZING  MIXTURES. 


Column  i  gives  the  name  of  the  principal  refrigerating  substance,  A  the  proportion  of  that  substance,  B  the  propor- 
tion of  a  second  substance  named  in  the  column,  C  the  proportion  of  a  third  substance,  D  the  temperature  of  the 
substances  before  mixture,  E  the  temperature  of  the  mixture,  .Fthe  lowering  of  temperature,  G  the  temperature 
when  all  snow  is  melted,  when  snow  is  used,  and  H  the  amount  of  heat  absorbed  in  heat  units  (small  calories  wheu 
A  is  grammes).  Temperatures  are  in  Centigrade  degrees. 


Substance. 

A 

B 

C 

D 

E 

F 

G 

H 

NaC2H3O2  (cryst.) 

85 

H2O-ioo 

_ 

10.7 

—  4-7 

154 

_ 

_ 

NH4C1  . 

30 

««       « 

— 

I3-3 

—  5-1 

18.4 

— 

— 

NaNO3  . 
Na2S2O8  (cryst.)    . 

75 
no 

«    !! 

— 

13.2 
10.7 

-U 

18.5 
18.7 

— 

— 

KI. 

140 

«    « 

— 

10.8 

—  11.7 

22.5 

- 

— 

CaCl2  (cryst.) 

250 

«    « 

- 

10.8 

—  12.4 

23.2 

_ 

_ 

NH4NO8       . 

60 

««    u 

— 

13.6 

-13.6 

27.2 

_ 

_ 

(NH4)2S04   .        . 

25 

;;   50 

NH4NO3-25 

26.0 

- 

- 

NH4C1  . 

25 

•t          <( 

— 

— 

22.0 

— 

— 

CaCl2    . 

«    « 

"          " 

_ 

_ 

20.0 

_ 

_ 

KNO8   . 

25 

«    « 

NH4Cl-25 

- 

- 

2O.O 

- 

- 

Na2SO4 

25 

«    « 

«             a 

— 

— 

19.0 

— 

— 

NaNO8. 

25 

«    « 

«             .( 

— 

— 

17.0 

— 

— 

K2SO4  . 

IO 

Snow  100 

_ 

— 

—  1.9 

0-9 

_ 

Na2CO3  (cryst.)     . 

20 

«        « 

_ 

— 

—  2.O 

I.O 

_ 

_ 

KN08   .        .        . 

13 

«        « 

- 

— 

-2.85 

I.8S 

- 

- 

CaCl2    . 

3° 

«        « 

— 

— 

—  10-9 

9-9 

— 

— 

NH4C1  . 
NH4N08 

25 
45 

«        « 

— 

— 

-15-4 
—  16.75 

14.4 

15-75 

_ 

_ 

NaNO3  . 

50 

<«        «< 

- 

— 

—  17.75 

16.75 

- 

- 

NaCl     . 

33 

«        «< 

— 

— 

—  21.3 

20.3 

— 

— 

"     1.097 

- 

— 

—  37-0 

36.0 

—  37-0 

0.0 

"     1.26 

— 

— 

—  36.0 

35-o 

—  30.2 

17.0 

H2S04+H20 
(66.1  %  H2S04) 

"     1-38 
"     2.52 
"     4-32 

- 

— 

—  35-0 
—  30.0 
—  25.0 

34-o 
29.0 
24.0 

—  25.0 
—  12.4 
—  7-o 

27.0 
133-0 
273.0 

'<     7.92 

— 

— 

—  2O.O 

19.0 

—  3-1 

553-o 

"    13.08 

- 

— 

—  16.0 

15.0 

—  2.1 

967.0 

"     0.35 

- 

0 

- 

0.0 

52.1 

"       49 

— 

o 

— 

— 

—  197 

49-5 

"       .61 

— 

0 

— 

— 

—  39-0 

40-3 

CaCl2  +  6H20      - 

«       .70 
"       .81 

: 

0 

o 

*" 

I 

—  54-9t 
—  40-3 

30.0 
46.8 

"     1-23 

- 

0 

- 

- 

—  21.5 

88.5 

"     2.46 

- 

0 

— 

- 

—  9.0 

192.3 

4.92 

— 

0 

— 

— 

—  4.0 

392-3 

Alcohol  at  4°       j 

77 

"  73 
CO2  solid 

: 

0 

—  30.0 
—  72.0 

"~ 

: 

Chloroform   . 

_ 

«       « 

_ 

_ 

—  77.0 

_ 

_ 

_ 

Ether     . 

_ 

«       « 

_ 

_ 

—  77.0 

*. 

_ 

_ 

Liquid  SO3    . 

_ 

«       « 

_ 

_ 

—  82.0 

- 

_ 

_ 

H20-.7S 

- 

20 

5.0 

- 

- 

33-o 

"     -94 

— 

20 

—  4.0 

— 

— 

21.0 

«       « 

- 

10 

—  4.0 

- 

- 

34-0 

"       " 

— 

5 

—  4.0 

— 

— 

40-5 

Snow     " 

_ 

o 

—  4.0 

— 

_ 

122.2 

NH4NO3       . 

H2O-i.20 

- 

10 

—  14-0 

- 

- 

17.9 

Snow     " 

— 

0 

—  14.0 

— 

_ 

129.5 

H2O-i.3i 

Snow     " 

: 

10 
0 

: 

: 

IO.O 

I3I-9 

H20-3.6i 

- 

10 

—  8.0 

- 

- 

0.4 

Snow     " 

o 

—  8.0 

327.0 

*  Compiled  from  the  results  of  Gailletet  and  Colardeau,  Hammerl,  Hanamann,  Moritz,  Pfanndler,  Rudorf,  and 
Tollinger. 

t  Lowest  temperature  obtained. 

SMITHSONIAN  TABLES. 


TABLE  218. 


221 


CRITICAL  TEMPERATURES,  PRESSURES,  VOLUMES,  AND 'DENSITIES  OF 

GASES.* 

6  =  Critical  temperature. 
p  =  Pressure  in  atmospheres. 

<j>  =  Volume  referred  to  air  at  o°  and  76  centimetres  pressure. 
d  =  Density  in  grammes  per  cubic  centimetre. 


Substance. 

9 

P 

* 

d 

Observer. 

Air     . 

—  140.0 

39-° 

_ 

_ 

Olszewski. 

Alcohol  (C2H6O) 

243.6 

62.76 

0.00713 

0.288 

Ramsay-  Young. 

<«             i< 

237-9 

— 

— 

— 

Mean  of  ten. 

"       (CH40) 

239-95 

78.5 

- 

- 

Young. 

Ammonia  . 

130.0 

115.0 

_ 

_ 

Dewar. 

Argon 

—  I2I.O 

50.6 

_ 

r-5 

Olszewski. 

Benzol 

288.5 

47-9 

0.00981 

°-3°5 

Young. 

Bromine     . 

3O2.2 

0.00605 

1.18 

Nadejdine. 

Carbon  dioxide  . 

30.92 

77 

0.0066 

— 

Andrews. 

"       monoxide 

—I4I.I 

35-9 

_ 

_ 

Wroblewski. 

"       disulphide 
Chloroform 
Chlorine 

277-7 
260.0 
I4I.O 

78.1 

54-9 
»3-9 

; 

- 

Hannay. 
Sajotschewsky. 
Dewar. 

« 

146.0 

_ 

_ 

Knietsch. 

Ether 

197.0 

35-77 

o.oi  584 

0.208 

Battelli. 

M 

1944 

35-6i 

0.01344 

0.262 

Young. 

Ethane 

35-0 

45-2 

_ 

Dewar. 

Ethylene 

9-2 

58.0 

_ 

_ 

Van  der  Waals. 

• 

13.0 

0.00569 

0.21 

Cailletet. 

Helium 

<—  264.0 

_ 

— 

—     • 

Dewar. 

Hydrogen 

•—234.5 

2O.O 

— 

_ 

Dewar. 

chloride 

5!-25 

86.0 

_ 

_ 

Ansdell. 

«               «« 

52-3 

86.0 

_ 

0.61 

Dewar. 

"         sulphide 

1  00.0 

88.7 

_ 

_ 

Olszewski. 

Krypton     . 
Methane    . 

-62.3 
—81.8 

54-3 
54-9 

: 

: 

Ramsey-Travers. 
Olszewski. 

« 

—99-5 

50.0 

_ 

_ 

Dewar. 

Neon  . 
Nitric  oxide  (NO) 

<—  205.0 
—93-5 

71.2 

: 

: 

Ramsey-Travers. 
Olszewski. 

Nitrogen    . 

—146.0 

35-o 

_ 

0.44 

« 

"       monoxide   N2O 

354 

75-° 

0.0048 

0.41 

Dewar,  Cailletet. 

Oxygen 
Sulphur  dioxide 

—118.0 
J554 

50.0 
78.9 

0.00587 

0.6044 
0.49 

Wroblewski. 
Sajotschewsky,  Cailletet. 

Water 

358.1 

0.001874 

0.429 

Nadejdine. 

H 

364-3 

194.6 

0.00386 

Batelli. 

Andrews,  Trans.  Roy.  Soc.  166,  1876.                 Olszewski,  C.  R.  98,  1884  ;  99,  1884  ;  100,  1885  ; 

Ansdell,  Chem.  News,  41,  1880.                                Beibl.  14,  1890;  Z..  Phys.  Ch.  16,  1893. 

Batelli,  Mem.  Torino  (2),  41,  1890.                       Ramsay-Young,  Tr.  Roy.  Soc.  177,  1886. 

Cailletet,  C.  R.  85,  1877  ;  C.  R.  94,  1882.           Sajotschewsky,  Beibl.  3,  1879. 
Dewar,  Phil.  Mag.  18,  1884  ;  Ch.  News,  84,     Van  der  Waals,  Beibl.  4,  1880. 

1901.                                                                    Wroblewski,  Wied.  Ann.  20,  1883;  Stz.  Wien. 

Hannay,  Pr.  Roy.  Soc.  32,  1882.                              Ak.  91,  1885. 
Knietsch,  Lieb.  Ann.  259,  1890.                           Young,  Phil.  Mag.  1900. 

Nadejdine,  Beibl.  9,  1885. 

*  Abridged  for  the  most  part  from  Landolt  and  Bernstein's  "  Phys._Chem.  Tab.' 
SMITHSONIAN  TABLES. 


222 


TABLE  219. 
COEFFICIENTS  OF  THERMAL  EXPANSION. 

Coefficients  of  Linear  Expansion  of  the  Chemical  Elements. 


In  the  heading  of  the  columns  T  is  the  temperature  or  range  of  temperature ;  C  is  the  coefficient 
of  linear  expansion ;  A\  is  the  authority  for  C;  Mis  the  mean  coefficient  of  expansion  between 
o°  and  100°  C. ;  o  and  ft  are  the  coefficients  in  the  equation  /«  — /0  (i  +  <^  +  ftt>2)>  where  /o  is 
the  length  at  o°  C.  and  /«the  length  at  (°  C. ;  A2  is  the  authority  for  a,  ft,  and  m. 


Substance. 

T 

CXio* 

^1 

MX  io« 

aX  10* 

/3  X  io« 

^ 

Aluminum        .... 

40 
600 

0.2313 

-31  CQ 

I 

•7 

O.222O 

- 

J>    r 

2 

« 

—  191  to  -|-i6 

i87S 

23C"?6 

OO7O7 

Antimony: 
Parallel  to  crysU  axis  . 
Perp.  to  axis 

40 
40 

4O 

•1UOJ 

.1092 

.0882 

1  1  C2 

I 
I 
J 

ictcfi 

'^JOJV 
OQ23 

.ww/w/ 
OI72 

6 

Arsenic     
Bismuth  : 
Parallel  to  axis     . 
Perp.  to  axis 

40 

40 
40 
4O 

.1.15*. 
•0559 

.1621 
.1208 
.1746 

I 

I 
I 
I 

1716 

*JSr*j 

.1167 

OI4Q 

6 

Cadmium         ...» 
Carbon  : 
Diamond      .... 
Gas  carbon  .        . 
Graphite       .... 
Anthracite    .... 
Cobalt      .'.... 

40 

40 
40 
40 
40 
40 

.1  j^u 
.3069 

.0118 

.0540 
.0786 
.2078 
.1236 

I 

I 
I 

I 

I 

.*  J1V 

•3159 

.2693 

.0466 

6 

40 

1678 

J 

1666 

1481 

0185 

6 

••  "-IQI  to     |    l6 

I4OQ 

16070 

Gold         

4O 

1443 

I 

I47O 

mS 

OI  12 

g 

AQ 

4I7O 

J 

Iron  : 
Soft       

4O 

.I2IO 

I 

Cast      

40 

1061 

J 

« 

Wrought      !        !        '.        ! 
Steel     

—  191  to  +16 
—  18  to  100 

AQ 

.0850 
.1140 

.1722 

4 
7 

- 

.11705 

OQI73 

.005254 

008  m6 

8 
8 

"    annealed 
Lead        .... 

40 

AQ 

.1095 
2Q24 

i 
j 

.1089 
27OQ 

.1038 
O277 

.0052 

I 

Magnesium      .... 
Nickel      

40 

AQ 

.2694 
1  270 

i 
i 

I  346o 

OO77I  C 

g 

« 

—  191  to  -}~i6 

.IOI2 

•woo1  5 

AQ 

.06^7 

i 

Palladium         .... 
Phosphorus      .... 

40 
O-4O 
4O 

.1176 

1.2530 

o  0800 

10 

i 

— 

.11670 
.0^868 

.002187 

OOI724 

8 
8 

Potassium        .... 
Rhodium          .... 

Ruthenium       .        .        . 

0-50 
40 
40 
AQ 

„ 
.0960 

.7680 

ii 

i 
i 

i 

.6604 

L 

12 

Silicon      ..... 

AQ 

JWV 

.0767 

i 

Silver       

4O 

.IQ2I 

i 

.18270 

.004707 

8 

H 

—  191  to  -f-i6 

.I7O4 

Sulphur  : 
Cryst  mean  .... 
Tellurium         .... 
Thallium          .... 
Tin  

40 
40 
40 

4O 

.6413 
•1675 
.3021 
.2274 

i 
i 
i 

i 

I.lSo 
.3687 

.22Q6 

.2O77 

.0263 

12 

12 

6 

Zinc  

AQ 

2Ql8 

";: 

2Q7O 

^741 

0274. 

6 

1  Fizeau. 

2  Calvert,  Johnson 

and  Lowe. 

3  Chatelier. 


4  Henning. 

5  Dittenberger, 

6  Matthiessen. 


Andrews. 
Hoi  born- Day. 
Benoit. 


10  Pisati  and  De 

Franchis. 

11  Hagen. 

12  Spring. 


The  above  table  has  been  partly  compiled  from  the  results  published  by  Fizeau,  "  Comptes  Rendus,"  vol.  68,  and 

Matthiessen,  "  Proc.  Roy.  Soc.,"  vol.  15. 
The  Holborn-Day  data  are  for  temperatures  from  20°  to  1000°  C.    The  Dittenberger,  o°  to  600°  C. 

SMITHSONIAN  TABLES. 


TABLE  220. 
COEFFICIENTS  OF  THERMAL   EXPANSION. 

Coefficients  of  Linear  Expansion  for  Miscellaneous  Substances. 


223 


The  coefficient  of  cubical  expansion  may  be  taken  as  three  times  the  linear  coefficient.     T  is  the  temperature  or  range 
of  temperature,  C  the  coefficient  of  expansion,  and  A  the  authority. 


Substance. 

^c. 

CXio* 

A. 

Substance. 

r°c. 

CXro* 

A. 

Brass  : 

Platinum-silver  : 

Cast     . 

O-IOO 

0.1875 

I 

lPt+2Ag 

O-IOO 

0.1523 

4 

Wire    . 

« 

0.1930 

I 

Porcelain 

20-790 

0.0413 

19 

—       ... 

" 

•  i  783--  i  93 

2 

"         Bayeux    . 

1000-1400 

0.0553 

20 

7i.5Cu+27.7Zn+ 

Quartz  : 

o.3Sn+o.5Pb 

40 

0.1859 

3 

Parallel  to  axis    . 

0-80 

0.0797 

6 

7iCu+29Zn 

O-IOO 

0.1906 

4 

«                it           tl 

—  19010+16 

0.1070 

21 

Bronze  : 

Perpend."     " 

0-80 

0.1337 

6 

3Cu+iSn    . 
tt        « 

16.6-100 
16.6-350 

0.1844 
0.2116 

5 
5 

Quartz  glass    . 
Rock  salt 

—  19010+16 
40 

—  .0026 
0.4040 

*3 
3 

"        " 

16.6-957 

0.1737 

5 

Speculum  metal 

O-IOO 

0.1933 

i 

86.3Cu+9.7Sn+ 
4Zn 

40 

0.1782 

3 

Topaz: 
Parallel  to  lesser 

97.6Cu+      ,  hard 
2.2  Sn+    <     ft 

0.2P      <S°ft 

0-80 

(I 

0.1713 

0.1708 

6 
6 

horizontal  axis 
Parallel  to  greater 
horizontal  axis 

M 

0.0832 
0.0836 

8 
8 

Caoutchouc 

_ 

.657-.6S6 

2 

Parallel  to  verti- 

"... 

16.7-25.3 

0.770 

7 

cal  axis 

" 

0.0472 

8 

Constantino     . 

4-29 

0.4570 

Tourmaline  : 

Ebonite   . 

25.3-354 

0.842 

7 

Parallel  to  longi- 

Fluor spar  :  CaF2  . 

O-IOO 

0.1950 

8 

tudinal  axis 

M 

0.0937 

8 

German  silver 

" 

0.1836 

8 

Parallel    to   hori- 

Gold-platinum : 
2Au+iPt 
Gold-copper  : 

" 

0.1523 

4 

zontal  axis 
Type  metal      . 
Vulcanite 

M 

16.6-254 

0-18 

0.0773 
0.1952 
0.6360 

8 
5 

22 

2Au+iCu 

" 

0.1552 

4 

Wedgwood  ware 

O-IOO 

0.0890 

5 

Glass  : 

Wood: 

Tube    . 

• 

0.0833 

i 

Parallel  to  fibre  : 

"... 

« 

0.0828 

9 

Ash  . 

" 

0.0951 

23 

Plate    . 

« 

0.0891 

10 

Beech 

2-34 

0.0257 

24 

Crown  (mean) 

« 

0.0897 

10 

Chestnut  . 

0.0649 

24 

«... 

50-60 

0.0954 

ii 

Elm  . 

1 

0.0565 

24 

Flint     . 

" 

0.0788 

ii 

Mahogany 

1 

0.0361 

24 

Jenather-    16™  ) 
mometer  normal) 

O-IOO 

0.081 

12 

Maple       . 
Oak  . 

« 

0.0638 
0.0492 

24 
24 

S9m     . 

H 

0.058 

12 

Pine  . 

" 

0.0541 

24 

«           «< 

—19110+16 

0.424 

13 

Walnut     . 

' 

0.0658 

24 

Gutta  percha  . 
Ice  . 

20 
—  20  to  —  i 

1.983 
0.51 

15 

Across  the  fibre  : 
Beech 

ft 

0.614 

24 

Iceland  spar  : 

Chestnut  . 

ft 

0.325 

24 

Parallel  to  axis    . 

0-80 

0.2631 

6 

Elm  . 

0-443 

24 

Perpendicular    to 

Mahogany 

0.404 

24 

axis 

ft 

0.0544 

6 

Maple 

0.484 

24 

Lead-tin  (solder) 

Oak  . 

0-544 

24 

2Pb+iSn 

O-IOO 

0.2508 

i 

Pine  . 

0.341 

24 

Magnalium 

12-39 

0.238 

16 

Walnut     . 

0.484 

24 

Marble     . 

15-100 

0.117 

17 

Wax:  White  . 

10-26 

2.300 

25 

Paraffin   . 

0-16 

1.0662 

18 

" 

26-31 

3.120 

25 

16-38 

1.3030 

18 

tt 

3J-43 

4.860 

25 

"... 

38-49 

4.7707 

18 

"      .     •  . 

43-57 

15.227 

25 

Platinum-iridium 

loPt+iIr 

40 

0.0884 

3 

i  Smeaton.               8  Pfaff.                                  14  Russner.             20  Deville  and  Troost. 

2  Various.                  9  Deluc.                                 15  Mean.                  21  Scheel. 

3  Fizeau.                  10  Lavoisier  and  Laplace.     16  Stadthagen.         22  Mayer. 
4  Matthiessen.         ii  Pulfrich.                              17  Frohlich.             23  Glatzel. 

5  Daniell.                 12  Schott.                                18  Rodwell.             24  Villari. 

6  Benoit.                  13  Henning.                             19  Braun.                 25  Kopp. 

7  Kohlrausch. 

SMITHSONIAN  TABLES. 


224  TABLE  221 . 

COEFFICIENTS   OF   THERMAL   EXPANSION. 

Coefficients  of  Cubical  Expansion  of  some  Crystalline  and  other  Solids.* 

T  =  temperature  or  range  of  temperature,  C=  coefficient  of  cubical  expansion,  A  =  authority. 


Substance. 

T 

CX  10* 

A 

Antimony  .... 

O-IOO 

0.3167 

Matthieson. 

Beryl  

O—  ICO 

O.OIOC 

Pfaff. 

Bismuth      .... 

0.4000 

Kopp. 

Diamond    .        .        •        . 

40 

0.0354 

Fizeau. 

Emerald      .        .        *        . 

40 

0.0168 

• 

Fluor  spar  .... 

14-47 

0.6235 

Kopp. 

Garnet        .... 

O-IOO 

0.2543 

Pfaff. 

Glass,  white  tube 

O-IOO 

0.2648 

Regnault. 

"       green  tube 

O-IOO 

0.2299 

« 

"       Swedish  tube  . 

O-IOO 

0.2363 

« 

"       hard  French  tube    . 

O-IOO 

0.2142 

« 

"       crystal  tube      . 

O-IOO 

0.2IOI 

« 

"       common  tube  . 

0-1 

0.2579 

« 

"      Jena 

O-IOO 

0.2533 

Reichsanstalt. 

Ice      

—  20  to  —  i 

1.  12  CO 

Brunner. 

Iceland  spar 

50-60 

•+»y 

0.1447 

Pulfrich. 

Idocrase     .... 

O-IOO 

0.2700 

Pfaff. 

O—  IOO 

0.  1  C  CO 

Dulong  and  Petit. 

« 

O—  7OO 

u  •JJJ 
0.4410 

<<          «        <t 

Magnetite,  FegO* 

W      JW 

O-IOO 

W.4f.4f..L  W 

0.2862 

Pfaff. 

Manganic  oxide,  Mi^Os     • 

O-IOO 

0.522 

Playfair  and  Joule. 

Orthoclase  (adularia) 

O-IOO 

0.1794 

Pfaff. 

Porcelain    .... 

O-IOO 

0.1080 

Deville  and  Troost. 

Quartz        .... 

50-60 

0.3530 

Pulfrich. 

Rock  salt    .... 

50-60 

I.2I2O 

«< 

Spinel  ruby         .        . 

40 

0.1787 

Fizeau. 

Sulphur,  rhombic 

O-IOO 

2.2373 

Kopp. 

Topaz         .... 

O-IOO 

0.2137 

Pfaff. 

Tourmaline        .        . 

O-IOO 

0.2181 

« 

Zincite,  ZnO 

40 

0.0279 

Fizeau. 

Zircon         .... 

O-IOO 

0.2835 

Pfaff. 

*  For  more  complete  tables  of  cubical  expansion,  see  Clarke's  "  Constants  of  Nature,' 
(Smithsonian  Collections),  published  in  1876.  s 

SMITHSONIAN  TABLES. 


TABLE  222. 
COEFFICIENTS  OF  THERMAL  EXPANSION. 

Coefficients  of  Cubical  Expansion  of  Liquids. 


225 


This  table  contains  the  coefficients  of  expansion  of  some  liquids  and  solutions  of  salts.    When  not  otherwise  stated 
atmospheric  pressure  is  to  be  understood.     T  gives  the  temperature  range,  C  the  mean  coefficient  of  expansion 
for  range  T  in  degrees  C.,  and  Av  the  authority  for  C.    a,  /3,  and  y  are  the  coefficients  in  the  volume  equation 
vt  =  v0  (i  +  "^  +  P*2  +  y&)»  and  »*  the  mean  coefficient  for  range  o°-ioo°  C.,  and  A2  is  the  authority  for  these. 

Liquid. 

T 

c 

Xrooo 

A, 

•tn 

X  loo 

a  X  looo 

/3Xio« 

yXio« 

A, 

Acetic  acid      .    .    .    . 

i6°-io7° 
0-54 

—  15  to  +80 
0-80 

o-39 
18-39 
0-40 
0-40 
—  38  to  +70 
11-81 
—  7  to  +60 

18-25 
17-24 
—34  to  +60 
0-50 
0-50 
0-63 
—1510+38 

0-30 
0-30 
24-299 

36-157 
7-38 
24-120 

10-40 
20-78 

0-30 
0-30 
—  9  to  +106 
o-33 

.866 
.524 

.940 
.581 

.992 

I 
I 

I 
I 

2 

•'433 
.1616 

.1433 

ill 

.0506 
.0510 
.1468 

•1399 
.2150 

•0534 

.0489 
-0933 

.0742 

.0572 
.0477 

•0539 
•0577 
.0899 

.1039 
.1067 
.0611 
.0627 

.0489 
.0799 
.1051 

1.0630 
1.3240 

0.8900 
1.0414 
0.7450 
0.2928 

1.1856 
1.1763 
1.0382 

0.0788 
0.4238 
I.I398 

I.I07I 
I-5I32 
0.4853 

0.4460 
0.0625 
O.l8l82 
0.6821 

0.8340 
0.8994 
0.0213 

0-3599 
0.5408 

0.5758 
0.2835 
0.9003 
—.0643 

0.1264 
3.8090 

0.6573 
0.7836 
1.850 
17.900 

1.5649 

1-2775 
1.7114 

4.2742 
0.8571 
1.3706 

4.6647 
2.3592 
0.4895 

0.430 
8.710 
0.00078 
1.1405 

0.1073 
1.396 
10.462 
2.516 

1.075 

0.864 
5.160 

1-959 
8.505 

1.0876 
0.8798 

1.1846 
1.7168 
0.730 
11.87 

0.91  1  1 
0.8065 
0-5447 

1.9122 

r-7433 
4-0051 

—•539 
0.4446 

6.790 

3 
3 

4 

I 

6 

4 
5 
4 

7 
7 
4 

4 

1 

9 
9 
15 
ii 

7 

7 

12 
12 
13 

14 
9 

9 

12 

9 
9 
5 
i5 

Alcohol  : 
Amyl       

Ethyl,  sp.  gr.  .8095   . 
"    50  %  by  volume 

"    30%    '     " 
'    500  atmo.  press. 
"    3000   "         " 
Methyl         .         .     . 

Calcium  chloride  : 
CaCl2,  5.8  %  solution 
CaCl2,  40-9  %      "      • 
Carbon  disulphide   .     . 
500  atmos.  pressure  . 
3000     "           " 
Chloroform     .... 
Ether                .... 

Hydrochloric  acid  : 
HC1  -f  6.25H2O  .    . 
HCl+5oH2O     .    . 
Mercury           »    *    •    • 

Potassium  chloride  : 
KC1,  2.5  %  solution  . 

KC1,  24.3%      " 
Potassium  nitrate  : 
KN03,  5.3  %  sol'n 
KN03,  21.9%      " 
Phenol,  C6H6O   .     .     . 
Petroleum             .     .     . 

Sp.  gr.  0.8467  .     .     . 
Sodium  chloride  : 
NaCl,  i.  6%  solution. 
Sodium  sulphate  : 
Na2SO4,  24  %  sol'n  . 
Sodium  nitrate  : 
NaNOg,  36.2%  sol'n. 
Sulphuric  acid  : 
H2SO4    

H2SO4  +  5oH2O     . 
Turpentine      .... 
Water 

AUTHORITIES. 

i  Amagat.              4  Pierre.                   7  Decker.             10  Broch.             13  Pinette. 
2  Barrett.               5  Kopp.                    8  Emo.                 u  Spring.            14  Frankenheim. 
3  Zander.               6  Recknagel.           9  Marignac.         12  Nicol.              15  Scheel. 

SMITHSONIAN  TABLES. 


226 


TABLE   223. 
COEFFICIENTS  OF  THERMAL  EXPANSION, 

Coefficients  of  Expansion  of  Gases. 
Pressures  are  given  in  centimetres  of  mercury. 


Coefficient  at  Constant  Volume. 

Coefficient  at  Constant  Pressure. 

Coeffi- 

8 

Coeffi- 

-8 

Substance. 

Pressure 
cm. 

cient 
X 

e 

Substance. 

Pressure 
cm. 

cient 
X 

1 

100. 

1 

IOO. 

« 

Air         .y    . 

.6 

•37666 

I 

Air 

76. 

•3671 

3 

m        *          ' 

1-3 

.37172 

" 

M 

257- 

•3693 

"            ;         .         . 

IO.O 

.36630 

" 

"    0°-IOO°      . 

IOO.I 

.36728 

2 

"           »         . 

25-4 

.36580 

« 

Hydrogen   o°-ioo° 

1  00.0 

.36600 

" 

• 

75-2 

.36660 

u 

"              . 

200  Atm. 

.332 

9 

"   0°-IOO°     . 

IOO.I 

•36744 

2 

"... 

400     " 

•295 

M 

tt 

76.0 

•36650 

3 

" 

600     " 

.261 

U 

•          .          . 

200.0 

.36903 

"... 

800     " 

.242 

ft 

(( 

2000. 

.38866 

tt 

Carbon  dioxide 

76. 

.3710 

3 

tt 

IOOOO. 

.4100 

" 

"      0°-20° 

51.8 

.37128 

2 

Argon    . 

S'7 

.3668 

4 

"    0°-40° 

51.8 

.37100 

M 

Carbon  dioxide     . 

76.0 

•36856 

3 

"           "      0°-IOO° 

51.8 

•37073 

tt 

"        *'     . 

1.8 

•36753 

i 

«      0°-20° 

99-8 

•37602 

ft 

tt        tt 

5.6 

.36641 

tt 

"      0°-IOO° 

99-8 

•37410 

ft 

tt        tt 

74-9 

.37264 

u 

«           "      0°-20° 

137-7 

.37972 

tt 

"                 0°-20°* 

51-8 

.36985 

2 

"          "      0°-IOO° 

*37-7 

•37703 

tf 

o°-4o° 

51.8 

.36972 

tt 

*«       «    o°~7  5° 

2621. 

.1097 

6 

0°-IOO° 

51.8 

.36981 

tf 

"  64°-ioo° 

2621. 

•6574 

M 

«           «     0°-20° 

99.8 

•37335 

tt 

Carbon  monoxide  . 

76. 

.3669 

3 

"                 0°-IOO° 

99.8 

.37262 

tt 

Nitrous  oxide 

76. 

•3719 

"                 0°-IOO° 

Carbon  monoxide  . 

1  00.0 

76. 

.37248 
•36667 

5 
3 

Sulphur  dioxide     . 
tt             « 

76. 
98. 

•39°3 
•3980 

u 

Helium  . 

56.7 

.366;; 

4 

{o°-ii9° 

76. 

.4187 

IO 

Hydrogen  i6°-i32° 
I5°~iT° 

.0077 
.025 

.3328 
•3623 

6 
ti 

0°~-l62<> 

76. 
76. 

.4189 
.4071 

ft 

•47 

.3656 

" 

0°-200° 

76. 

•3938 

tt 

. 

•93 

.37002 

i 

o°-247° 

76. 

•3799 

ft 

. 

II.  2 

.36548 

" 

Nitrogen    13°-!  32° 
9°-i33° 

0°-20° 
0°-IOO° 

II 

76.4 
100.0 

.06 

•53 

100.2 
100.2 

tay? 

•36504 
.36626 
.3021 
•3290 
.36754 

2 

6 

2 

tt 

Thomson  has  given,  Encyc.  Brit.  "  Heat," 
the  following  for  the  calculation  of  the  ex- 
pansion, E,  between  o°  and  100°  C.  Expansion 
is  to  be  taken  as  the  change  of  volume  under 
constant  pressure  : 

Oxygen  n°-i32°    . 
"         90-132° 

"           II°-I32°     ! 

76. 
.007 
•25 
•51 

i.  0 

18.5 

.4161 
.3984 
•3831 
•36683 

I 

tt 
tt 

8 

Hydrogen,  E  =  .3662(1  —  .00049  F/#), 
Air,             .£  =  .3662(1  —  .0026  y/^t 
Oxygen,      £  =  .3662(1  —  .0032   V/v), 
Nitrogen,    .£  =  .3662(1  —  .0031    V/v), 
CO2             £•  =  .  3662(1  —  .0164  V/v). 

"... 

75-9 

."36681 

« 

V/v  is  the  ratio  of  the  actual  density  of  the 

Nitrous  oxide 

76 

'3676 

3 

gas  at  o°  C  to  what  it  would  have  at  o°  C  and 

Sulph'r  dioxide  SO2 

76. 

•3845 

n 

i  Atm.  pressure. 

I  Meleander,  Wied.  Beibl.  14,  1890;  Wied.           5  Chappuis,  Arch.  sc.  phys.  (3),  18,  1892. 
Ann.  47,  1892.                                                    6  Baly-Ramsay,  Phil.  Mag.  (5),  38,  1894. 

2  Chappuis,  Trav.  Mem.  Bur.  Intern.  Wts.          7  Andrews,  Proc.  Roy.  Soc.  24,  1876. 

Meas.  13,  1903.                                                  8  Meleander,  Acta  Soc.  Fenn.  19,  1891. 

3  Regnault,  Ann.  chim.  phys.  (3)5,  1842.               9  Amagat,  C.  R.  in,  1890. 
4  Keunen-Randall,  Proc.  R.  Soc.  59,  1896.         10  Him,  Theorie  mec.  chaleur,  -1862. 

SMITHSONIAN  TABLES. 


TABLES  224-226. 
MECHANICAL  EQUIVALENT  OF  HEAT, 

TABLE  224. -Summary. 


227 


Taken  from  J.  S.  Ames,  L'equivalent  mecanique  de  la  chaleur,  Rapports  presentes  au  congres 
international  du  physique,  Paris,  1900. 


Name. 

Method. 

Scale. 

Result. 

Temp.  °C. 

Joule    . 

Mechanical 

I6.C 

Rowland 

Mechanical 

IO. 

4.187 

'5- 

4-181 

20. 

4.176 

25. 

Reynolds-Morby  . 

Mechanical     . 

4.1872 

Mean- 

calory. 

Griffiths       .      -I 

Electrical 

(  Latimer-Clark=  I.4342V  at  15°  C. 

4.198 
4.192 

IS- 

20. 

E2t  . 
R 

(  International  Ohm 

4.187 

25- 

Schuster-Gannon 

Electrical  Eit. 

0~  atimer-Clark  =  I.434OV.  at  15°  ) 
:.,  Elec.  Chem.  Equiv.  Silver! 

4.1905 

19.1 

=  o.ooin8g                                ) 

C  all  endar-B  arnes 

Electrical  Eit. 

timer-Clark  =  I-4342V.  at  15°  C. 

4.179 

40. 

TABLE  225.  —  Reduced  to  Gramme-calory  at  20°  0.  (Nitrogen  thermometer). 


Joule     . 
Rowland 
Griffiths 
Schuster-Gannon  . 
Callendar-Barnes  . 

4.169  X  io7  ergs 
4.181        «      " 
4.192        «      « 
4.189        "      " 
4.186        "      " 

4.169  X  io7  ergs. 
4.181        "      " 
4.184        «      « 
4.181         "      " 
4.178        "      " 

*  Admitting  an  error  of  r  part  per  1000  in  the  electrical  scale. 

The  mean  of  the  last  four  then  gives 
1  small  (20°  G.)  calory  =  4.181  X  io7  ergs. 


TABLE  226. -Conversion  Factors  for  Units  of  Work. 


Joules 

Watts  per 
sec. 
Volt-amp. 

Small  20° 
Calories. 

Ergs. 

Kilo- 
gramme- 
metres. 

Foot-poundals. 

Foot-pounds. 

per  sec. 

i  joule  =  i  watt 
per  second 

I 

0.2392 

IO7 

T 

23.73 

23.73 
g 

i    small    20°  cal- 

orv  ~~—  • 

4.181 

I 

4.181  X  io7 

4-1" 

99.22 

99-23 

uijr  — 

g 

g 

i  erg  = 

io-7 

0.2392  X  io~7 

I 

IO-T 

g 

23-73  X  io-7 

!H3XIO-' 

i  kilog.-metre  = 

g 

0.2392g 

gX  io7 

I 

23-73g 

23-73 

i  foot-poundal  = 

.04214 

.01008 

421400. 

.04214 

g 

i 

I 
g 

i  foot-pound  = 

.042  1  4g 

.oiooSg 

4214008 

.04214 

g 

I 

SMITHSONIAN  TABLES. 


228 


TABLE  227. 
SPECIFIC  HEAT  OF  THE  CHEMICAL  ELEMENTS. 


Element. 

Range  *  of 
Temperature, 

Specific 
heat. 

j| 

Element. 

Range  *  of 
Temperature, 

Specific 
heat. 

Is 

Aluminum 

M 

—250 
O 

0.1428 
.2089 

i 

Iodine 
Iridium 

9-98 

—  i86-  +  i8 

0.0541 
.0282 

3 

*'                . 

IOO 

.2226 

" 

"            .         . 

18-100 

•0323 

« 

" 

250 

.2382 

" 

Iron,  cast  t 

20-100 

.1189 

27 

"                . 

500 

•2739 

" 

"      wrought  . 

15-100 

.1152 

28 

"                .               . 

10-100 

.2122 

43 

«                        (4 

IOOO-I2OO 

.1989 

u 

Antimony  . 

15 

.0489 

2 

«           «« 

500 

.176 

It 

" 

IOO 

•0503 

H 

'.'   hard-drawn 

0-18 

.0986 

29 

" 

200 

.O52O 

" 

u        ««           <« 

2O-IOO 

.1146 

" 

Arsenic,  gray    . 

O-IOO 

.0822 

3 

M 

—185-  +20 

.0958 

4 

black  . 

O-IOO 

.0861 

Lanthanum 

O-IOO 

.0448 

15 

Barium 

—  185-  +20 

.068 

4 

Lead 

15 

.0299 

2 

Bismuth    . 

—  186 

.0284 

5 

"             > 

IOO 

.0311 

" 

" 

O 

.0301 

6 

M 

300  • 

•0338' 

" 

. 

75 

.0309 

" 

"    '  fluid 

to  310 

•0356 

30 

" 

20-100 

.0302 

7 

"         "  . 

"  360 

.0410 

" 

"          fluid  . 

280-380 

•0363 

8 

H 

18-100 

.03096 

43 

Boron 

*    O-IOO 

9 

" 

16-256 

.03191 

it 

Bromine,  solid  . 

—  78  20 

'0843 

10 

Lithium     . 

—  IOO 

•5997 

31 

"         fluid  . 

13—45 

.107 

ii 

"           9 

O 

•795i 

(4 

Cadmium  . 

21 

•0551 

2 

u 

50 

.9063 

" 

.        . 

IOO 

" 

u 

IOO 

1.0407 

i( 

u 

200 

•0594 

M 

« 

190 

I-3745 

M 

Caesium     . 

300 
0-26 

.O6l7 
.0482 

12 

Magnesium 

—185-  +20 

60 

O.222 
.2492 

4 
7 

Calcium    . 

—185  1-20 

.157 

4 

" 

325 

•3235 

H 

. 

0-181 

.170 

"       .        . 

625 

•4352 

" 

Carbon,  graphite 

—5° 

.114 

14 

«« 

20-100 

.2492 

" 

"             "     . 

.160 

Manganese 

60 

.1211 

" 

«<             « 

977 

.467 

" 

" 

325 

.1783 

" 

"       diamond 

—5° 

.0635 

" 

" 

20-100 

.1211 

" 

«             « 

+  11 

•"3 

" 

'* 

—  IOO 

.0979 

31 

"             " 

985 

•459 

" 

M 

0 

.IO72 

M 

Cerium 

O-IOO 

.0448 

15 

"       . 

IOO 

•1143 

" 

Chlorine,  liquid 

0-24 

.2262 

16 

Mercury    . 

—185  1-20 

.032 

4 

Chromium 

—  200 

.0666 

17 

"           .        . 

O 

•03346 

3f 

« 

O 

.1039 

" 

85 

.0328 

" 

IOO 

.1121 

u 

H 

IOO 

.03284 

2 

H 

600 

.1872 

tf 

"                .            . 

250 

.03212 

* 

« 

—185-  +20 

.086 

4 

Molybdenum     . 

—185-  +20 

.062 

4 

Cobalt 

500 

.I452 

18 

" 

60 

.0647 

7 

"                  . 

IOOO 

.204 

" 

" 

475 

.0750 

it 

M 

—182-  +15 

15-100 

.0822 
.1030 

\? 

Nickel      .' 

20-100 
—185-  +20 

.0647 
.092 

« 

Copper 

17 

.0924 

2 

" 

IOO 

.1128 

18 

H 

IOO 

.0942 

u 

"           .        . 

300 

.1403 

* 

" 

15-238 

.09510 

43 

" 

500 

.1299 

«« 

" 

900 

.1259 

20 

"           .        . 

IOOO 

.1608 

« 

H 

—  i8i-+i3 

.0868 

21 

**           ,        . 

i  8-ioo 

.109 

26 

« 

23-100 

.0940 

" 

Osmium    . 

19-98 

.0311 

10 

Gallium,  liquid  . 

to  113 

.080 

22 

Palladium  . 

—  i86-+i8 

.0528 

26 

"        solid   . 

12-23 

.079 

22 

"         m        . 

O-IOO 

.0592 

24 

Germanium 

O-IOO 

•0737 

23 

«        , 

0-1265 

.0714 

M 

Gold  . 

—  igt-    -|_2O 

•°33 

4 

Phosphorus,  red 

0-51 

.1829 

33 

Indium 

O-IOO 
O-IOO 

.0316 
.0570 

24 

"      yellow 
(i          «• 

—i  86-  +20 

.202 

.178 

« 

4 

See  opposite  page  for  References. 

*  Where  one  temperature  alone  is  given,  the  "  true  "  specific  heat  is  given ;  otherwise,  the  "  mean  "  specific  heat. 
t  See  Appendix.    Tables  334~335. 
SMITHSONIAN  TABLES. 


TABLES  227  (c*«i'/>t 

SPECIFIC   HEAT. 

TABLE  227.— Specific  Heat  of  the  Chemical  Elements  (continued). 


229 


Element. 

Range  *  of 
Temperature,  °C. 

Specific 
Heat. 

Refer- 
ence. 

Element. 

Range  *  of 
Temperature,  °C. 

Specific 
Heat. 

Refer- 
ence. 

Platinum 

-I86-+I8 
o-ioo 

100 
500 

700 
900 

1  100 

1500 
500 

IIOO 

0.0293 
.0323 
.0275 
.0356 
.0368 
.0380 
.0390 
.0407 
.0335 
.0358 
0368 

26 
24 
34 
35 

Sulphur     .    .    . 
rhombic 
"       monoclin 
liquid  . 
Tantalum     .    . 
Tellurium     .    . 
crys. 
Thallium  .    .    . 

Thorium  .    .    . 
Tin                .    . 

-I88-+I8 
0-54 
0-52 
II9-I47 
—  185-+20 
—  i88-+i8 
15-100 
—  185—1-20 

20-100 
O-IOO 
—  196  —  79 

0.137 
.1728 
.1809 
.235 
.033 
.047 
.0483 
.038 
.0326 
.0276 
.0486 

36 
33 

2 

36 
37 
4 
27 
38 
26 

—  185  —  I-2O 

170 

4 

—  76-+I8 

.0518 

Rhodium 
Ruthenium 
Selenium 
Silicon 

Silver 

10-97 
o-ioo 
—  I88-+I8 

—  185-+  20 
-39-8 
+  57.1 

232 

-i  86  —  79 
-79-+I8 

.0580 
.0611 
.068 

.1360 
.1833 
.2029 
.0496 
•0544 

25 

3 

4 
14 

26 

"    cast     .    .    . 

!',  flu.id  •  •  • 

Titanium  .    .    . 
Tungsten  .    .    . 

Uranium  .    .    . 
Vanadium     .    . 
Zinc 

21-109 
250 
IIOO 

—185  —  (-20 

O-IOO 
—  185-+20 
O-IOO" 

0-98 

O-IOO 
—  192  —  I-2O 

.0551 
.05799 
.0758 
.082 
.1125 
.036 
.0336 
.028 
•1153 
.0836 

30 

18 

4 
39 
4 
40 
41 
40 
27 

„ 

O5498 

2 

2O-IOO 

.0931 

„ 

14 

o—  100 

.0935 

13 

•  4       ' 

44 

IOO 

0951 

2 

44 

17—  S07 

05987 

43 

44 

2OO 

.0996 

,4 

8OO 

18 

44 

3OO 

.1040 

44 

"      fluid 
Sodium  . 

907-1100 

—  I8S-+20 

.0748 
.253 

4 

Zirconium     .    .    . 

O-IOO 

.0660 

42 

1  Bontschew. 

2  Naccari,  Atti  Torine,  23,  1887-88. 

3  Wigand,  Ann.  d.  Phys.  (4)  22,  1907. 

4  Nordmeyer-Bernouli,  Verh.  d.  phys.  Ges.  9,  1907 ;  10, 

1908. 

5  Giebe,  Verh.  d.  phys.  Ges.  5,  1903. 

6  Lorenz,  Wied.  Ann.  13,  1881. 

7  Stucker,  Wien.  Ber.  114,  1905. 

8  Person,  C.  R.  23,  1846;  Ann.  d.  chim.  (3)21,  1847; 

24,  1848. 

9  Moisson-Gautier,  Ann.  chim.  phys.  (7)  17,  1896. 

10  Regnault,  Ann.  d.  chim.  (3)  26,  1849 ;  63,  1861. 

11  Andrews,  Pog.  Ann.  75,  1848. 


12  Eckardt-Graefe,  Z.  Anorg.  Ch.  23,  1900. 

13  Bunsen,  Pogg.  Ann.  141,  1870;  Wied.  Ann.  31 

14  Weber,  Phil.  Mag.  (4)  49,  1875. 

15  Hillebrand,  Pog.  Ann.  158,  1876. 

16  Knietsch. 

17  Adler,  Beibl.  27,  1903. 

18  Pionchon,  C.  R.  102-103,  1886. 

19  Tilden,  Phil.  Trans.  (A)  201,  1903. 

20  Richards,  Ch.  News,  68,  1893. 

21  Trowbridge,  Science,  8,  1898. 


1887. 


22  Berthelot,  Ann.  d.  chim.  (5)  15,  1878. 

23  Pettersson-Hedellius,  J.  Pract.  Ch.  24,  1881. 

24  Violle,  C.  R.  85,  1877 ;  87,  1878. 

25  Regnault,  Ann.  d.  chim.  (2)  73,  1840 ;  (3)  63,  1861. 

26  Behn,  Wied.  Ann.  66,  1898  ;  Ann.  d.  Phys.  (4)  i,  1900. 

27  Schmitz,  Pr.  Roy.  Soc.  72,  1903. 

28  Nichol,  Phil.  Mag.  (5)  12,  1881. 

29  Hill,  Verh.  d.  phys.  Ges.  3,  1901. 

30  Spring,  Bull,  de  Belg.  (3)  n,  1886;  29,  1895. 

31  Laemmel,  Ann.  d.  Phys.  (4)  16,  1905. 

32  Barnes-Cooke,  Phys.  Rev.  16,  1903. 

33  Wiegand,  Fort.  d.  Phys.  1906. 

34  Tilden,  Pr.  Roy.  Soc.  66,  1900,  71,  1903 ;  Phil.  Trans. 

(A)  194,  1900;  201,  1903. 

35  White,  Phys.  Rev.  28,  1909. 

36  Dewar,  Ch.  News,  92,  1905. 

37  Kopp,  Phil.  Trans.  London,  155,  1865. 

38  Nilson,  C.  R.  96,  1883. 

39  Nilson-Pettersson,  Zt.  phys.  Ch.  i,  1887. 

40  Mache,  Wien.  Ber.  106,  1897. 

41  Blumcke,  Wied.  Ann.  24,  1885. 

42  Mixter-Dana,  Lieb.  Ann.  169,  1873. 

43  Magnus,  Ann.  d.  Phys.  31,  1910. 


*  When  one  temperature  alone  is  given,  the  "  true  "  specific  heat  is  given ;  otherwise,  the  "  mean  "  specific  heat. 
Compiled  in  part  from  Landolt-Bornstein-Meyerhoffer's  Physikalisch-chemische  Tabelleu. 

TABLE  228.— Specific  Heat  of  Water  and  of  Mercury. 


Specific  Heat  of  Water. 

Specific  Heat  of  Mercury. 

Temper- 
ature,°C. 

Barnes. 

Rowland. 

Barnes- 
Regnault. 

Temper- 
ature,°C. 

Barnes. 

Barnes- 
Regnault. 

Temper- 
ature,°C. 

Specific 
Heat. 

Temper- 
ature,°C. 

Specific 
Heat. 

—5 

i.oiSS 

_ 

_ 

60 

0.9988 

0.9994 

O 

0.03346 

90 

0.03277 

o 

1.00914 

- 

1.0094 

65 

•9994 

1.0004 

5 

.03340 

IOO 

.03269 

+5 

1.0050 

1.0054 

1.0053 

70 

I.OOOI 

1.0015 

10 

.03335 

no 

.03262 

10 

I.OO2O 

1.0019 

1.0023 

80 

1.0014 

1.0042 

IS 

.03330 

120 

.03255 

15 

1.0,000 

1.  0000 

i  .0003 

90 

1.0028 

1.0070 

20 

.03325 

130 

.03248 

20 

0.9987 

0.9979 

0.9990 

IOO 

1.0043 

I.OIOI 

25 

.03320 

140 

.03241 

25 

.9978 

.9972 

.9981 

120 

1.0162 

30 

.03316 

ISO 

.0324 

30 

•9973 

.9969 

•9976 

140 

— 

1.0223 

35 

.03312 

170 

.0322 

35 

.9971 

.9981 

.9974 

1  60 

- 

1.0285 

40 

.03308 

190 

.0320 

40 

•9971 

•9974 

1  80 

— 

1.0348 

50 

.03300 

2IO 

.0319 

45 

•9973 

_ 

•9976 

2OO 

- 

1.0410 

60 

.03294 

- 

50 

•9977 

• 

.9980 

220 

— 

1.0476 

70 

.03289 

— 

— 

55 

.9982 

~ 

.9985 

" 

: 

I 

80 

.03284 

" 

" 

Barnes's  results:  Phil.  Trans.  (A)  199,  1902;  Phys.  Rev.  15,  1902;  16,  1903.     (H  thermometer.) 
Rowland's  as  revised  by  Pernet.     (H  thermometer.)  Barnes-Regnault's  as  revised  by  Peabody ;  Steam  Tables. 

The  mercury  data  from  o°  C  to  80,  Barnes-Cooke  (H  thermometer);  from  90°  to  140,  mean  of  Winklemann,  Nac- 
cari and  Milthaler  (air  thermometer);  above  140°,  mean  of  Naccari  and  Milthaler. 

SMITHSONIAN  TABLES. 


230 


TABLES  229-230. 
TABLE  229.  — Specific  Heat  of  Various  Solids.* 


Solid. 

Temperature 
*C. 

Specific  Heat. 

Authority.! 

Alloys  : 
Bell  metal         

Tc-o8 

o  08  58 

R 

ijyv 

o 

L 

"      yellow    

o 

08831 

«( 

I4_n8 

0862 

R 

88.7  Cu-f-ii.3  Al      

2O-IOO 

.IOJ.72 

Ln 

German  silver  
Lipowitz  alloy:  24.97  Pb  -f-  10.13  Cd  +  50-66  Bi 
+14-24  Sn         .        .        .        . 

0-100 

5-50 
IOO—I5O 

.09464 

•0345 
.0426 

T 

M 
ft 

Rose's  alloy  :  27.5  Pb+48.9  Bi-J-23.6  Sn 

Wood's  alloy:  '25.85  Pb  '+  6.99  Cd  +  52.43  Bi  + 

14-73  Sn  
"           "       (fluid)       

—77-20 
20-89 

5-50 
100-150 

•0356 
•0552 

.0352 

.O42O 

S 

«< 

M 
« 

Miscellaneous  alloys  : 
17.5  Sb+29.9  Bi+i8.7  Zn+33-9  Sn 
37.1  Sb-j-62-9  Pb      

20-99 
10-08 

.03880 

R 
<t 

39.9  Pb-f-6o.i  Bi                                                . 

;.   -* 
lO-QQ 

.0116$ 

p 

"             "     (fluid)      

1  4.A-  1S>8 

.O^CQQ 

«« 

63.7  Pb+36-3  Sn      

I2-QQ 

.0407  ^ 

R 

46.7  Pb+53.3  Sn      

IO-QQ 

.04  HO7 

M 

63.8  Bi+36.2  Sn       

2O-QQ 

.O4OOI 

« 

2O—  QQ 

.04  CO4. 

<« 

2O-IO4O 

Glass,  normal  thermometer  i6m  
"     French  hard  thermometer         .... 

IQ-IOO 
IO-^O 

!i6i 

w 
z 

H  M 

"     flint    

IO-CQ 

.117 

M 

Ice        

« 

—  188  252 
_78  188 

*£ 

.146 
.2815 

D 
it 

« 

_!8  78 

x--5 

.463 

«< 

India  rubber  (Para)      
Paraffin         

?  -100 

—  2O  r~^ 

.481 
.3768 

G-T 
R  W 

« 

i    J 
—  IQ  h2O 

.^2^1 

si 

M 

O—  2O 

•3*0^ 
.OQ  T.Q 

H 

tt 

"       fluid.        '.        1        '.        '.        '.        '.        .'        '. 

35-40 

DO—  O'? 

.622 
.712 

B 

« 

Vulcanite      

2O-IOO 

.T-JI2 

A  M 

TABLE  230. -Specific  Heat  of  Various  Liquids.* 


Liquid. 

Temper- 
ature °C. 

Specific 
Heat. 

Author- 
ity. 

Liquid. 

Temper- 
ature °C. 

Specific 
Heat. 

Author- 
ity.t 

Alcohol,  ethyl  . 

—  20 

0.5053 

R 

Nitrobenzole 

28 

0.362 

A 

0 

•548 

" 

Napthalene,  CioHg 

80-85 

.396 

B 

"              . 

40 

.648 

* 

"            . 

90-95 

.409 

" 

"        methyl       . 

5-10 

•590 

" 

Oils  :  castor  . 

•434 

W 

.        . 

15-20 

.601 

* 

citron  . 

5-4 

438 

H  W 

Anilin       .... 

15 

•514 

G 

olive     . 

6.6  * 

.471 

" 

M 

30 

.520 

¥ 

sesame 

- 

•387 

W 

Benzole,  C6H6. 

50 
10 

.529 
•340 

H-D 

turpentine    . 
Petroleum 

0 

21-58 

.411 
•511 

R 
Pa 

"         .        .        .        . 

40 

423 

H 

Toluol,  C6H8 

IO 

•364 

H-D 

"         .... 

65 

.482 

" 

"... 

65 

.490 

" 

Diphenylamine,  CiaHnN 

.464 

B 

"       . 

8s 

•534 

a 

"          ... 

65 

.482 

" 

CaCl2,  sp.  gr.  1.14  . 

—i5 

.764 

DMG 

Ethyl  ether 

o 

•529 

R 

o 

•775 

M 

Glycerine          .        . 

15-50 

•  S76 

E 

«            «        «    ^ 

+  20 

•787 

" 

Nitrobenzole    . 

14 

•350 

A 

"                "       1.20. 

2O 

•695 

*  These  specific  heat  tables  are  compiled  partly  from  more  extended  tables  in  Landolt-Bbrnstein-Meyerhoffer's  Tables, 
t  For  references  see  Table  230,  page  231. 
SMITHSONIAN  TABLES. 


TABLES  230  (continuett)~23\ . 
TABLE  230. -Specific  Heat  of  Various  LiQuids. 


231 


Liquid. 

Tempera- 
ture °C. 

Specific 
Heat. 

Author- 
ity. 

Liquid. 

Tempera- 
ture °C. 

Specific 
Heat. 

Author- 
ity. 

CaCl2,  sp.  gr.  1.  2O  . 

0 

0.712 

DMG 

KOH  +  3oH2O. 

18 

0.876 

TH 

«              u         « 

+20 

.725 

" 

"       +100    "      . 

18 

•975 

0 

"        "    1.26  . 

—  2O 

.651 

" 

NaOH  +  50  H2O 

18 

.942 

" 

O 

.663 

"        +  100     "   . 

18 

•983 

«            i«        «     ^ 

+  20 

.676 

• 

NaCl+ioH20. 

18 

.791 

" 

CuSo4+5oH2O     . 

12-15 

.848 

Pa 

"      +200     "      . 

18 

.978 

" 

"        +200    " 

12-14 

•951 

" 

Sea  water,  sp.  gr.  1.0043 

*7-5 

.980 

«        +400    "            . 

13-17 

•975 

" 

"         "      1.0235 

.938 

ZnSO4+50  H2O    . 

20-52 

.842 

Ma 

"        -         «      1.0463 

17-5 

•903 

" 

"         +200    " 

20-52 

•952 

A,  Abbot.                        DMG,  Dickinson,  Mueller,  and  George.           T,  Tomlison. 

AM,  A.  M.  Mayer.          H-D,  de  Heen  and  Deruyts.                               S,  Schiiz. 

B,  Batelli.                        HM,  H.  Meyer.                                                     Th,  Thomsen. 

D,  Dewar.                       L,  Lorenz.                   P,  Person.                         W,  Wachsmuth. 

E,  Emo.                           Ln,  Luginen.               Pa,  Pagliani.                     Wn,  Winkelmann. 

G,  Griffiths.                      M,  Mazotto.                 R,  Regnault.                     Z,  Zouloff. 

G-T,  Gee  and  Terry.      Ma,  Marignac.            RW,  R.  W.  Weber. 

TABLE  231. -Specific  Heat  of  Minerals  and  Rocks. 


Substance. 

Tempera- 
ture °  C. 

Specific 
Heat. 

Refer- 
ence. 

Substance. 

Tempera- 
ture °  C. 

Specific 
Heat. 

Refer- 
ence. 

Andalusite     . 

O-IOO 

0.1684 

, 

Rock-salt      . 

*3-45 

0.219 

6 

Anhydrite,  CaSO4 

O-IOO 

.1753 

I 

Serpentine    . 

16-98 

.2586 

2 

Apatite  .... 

15~99 

.1903 

2 

Siderite 

9-98 

•1934 

4 

Asbestos 
Augite   .... 

20-98 
20-98 

•195 

•I93I 

3 
3 

Spinel  . 
Talc      . 

15-47 
20-98 

.194 
.2092 

6 

3 

Barite,  BaSO4 

10-98 

.1128 

4 

Topaz  . 

O-IOO 

.2097 

i 

Beryl      .... 

X5~99 

.1979 

2 

Wollastonite 

I9~5I 

.178 

6 

Borax,  Na2B4O7  fused 

16-98 

•2382 

4 

Zinc  blende,  ZnS  . 

O-IOO 

.1146 

i 

Calcspar,  CaCO8  . 

0-50 

.1877 

i 

Zircon  . 

21-51 

.132 

6 

"               "       .        . 

O-IOO 

.2005 

i 

Rocks  : 

"               " 

0-300 

.2204 

i 

Basalt,  fine,  black 

12-100 

.1996 

6 

Casiderite,  SnO8    . 

16-98 

•0933 

4 

"         "        " 

2O-47O 

.199 

9 

Corundum 
Cryolite,  Al2Fl6.6NaF  . 

9-9* 
16-99 

.1976 

.2522 

4 

2 

"         «    .    « 

470-750 
750-880 

•243 
.626 

9 
9 

Fluorite,  CaF2 
Galena,  PbS  . 

15-99 

O-IOO 

•2154 
.0466 

4 
5 

it        «         « 
Dolomite    . 

880-1190 
20-98 

•323 
.222 

9 
3 

Garnet    .... 

16-100 

•1758 

2 

Gneiss 

17-99 

.196 

10 

Hematite,  Fe2Os  . 

15-99 

.1645 

2 

" 

17-213 

.214 

10 

Hornblende  . 

20-98 

•  1952 

3 

Granite 

I2-IOO 

.192 

7 

Hypersthene  . 

20-98 

.1914 

3 

Kaolin 

20-98 

.224 

3 

Labradorite 

20-98 

.1949 

Lava,  Aetna 

23-100 

.2OI 

n 

Magnetite 

18-45 

.15? 

6 

"          "   . 

31-776 

•259 

ii 

M  alachite,  C  u2C  O4.  H2O 

T5~99 

.1763 

2 

"      Kilauea    . 

25-100 

.197 

ii 

Mica  (Mg)     . 

20-98 

.2061 

3 

Limestone  . 

15-100 

.216 

12 

"     (K)        .'       .        . 

20-98 

.2080 

3 

Marble 

O-IOO 

.21 

— 

Oligoclase 

20-98 

.2048 

3 

Quartz  sand 

20-98 

.191 

3 

Orthoclase 

15-99 

.1877 

2 

Sandstone  . 

- 

.22 

Pyrites,  copper 

1S~99 

.1291 

2 

Pyrolusite,  MnO2  . 
Quartz,  S5O2 

17-48 

I2-IOO 
O 

.1717 

O£. 

6 

8 

i  Lindner.       6  Kopp.          n  Bartoli. 
2  Oeberg.        7  Joly.             12  Morano. 
3  Ulrich.         8  Pionchon. 

it                   H 

35° 

.2786 

8 

4  Regnault.     9  Roberts-  Austen,  Rticker. 

•               •               • 

400-1200 

•305 

8 

5  Tilden.        10  R.  Weber. 

Compiled  from  Landolt-Bornstein-Meyerhoffer's  Physikalisch-chemische  Tabellen. 
SMITHSONIAN  TABLES. 


232 


TABLE  232. 
SPECIFIC   HEATS   OF   GASES  AND   VAPORS, 


Substance. 

Range  of 
emp.  °C. 

Sp.  Ht. 
Constant 
Pressure. 

Authority. 

Range  of 
Temp.°C. 

Mean 
Ratio  of 
Specific 
Heats. 

Cp/CT. 

Authority. 

Acetone,  C8H6O  . 

26-IIO 

0.3468 

Wiedemann. 

«             « 

27-179 

0.3740 

M 

i(                         «< 

29-233 

0.4125 

Regnault. 

Air                .        .        . 

30-  +  10 

0.2377 

«( 

5-H 

1.4025 

Lummer  and 

'        '        ' 

O-IOO 

0.2374 

« 

Pringsheim. 

"        •  -  :    . 

0-200 

0.2375 

" 

"                 ... 

20-440 

0.2366 

Holborn  and 

"                 ... 

20-630 

0.2429 

Austin. 

"                 ... 

20-800 

0.2430 

<« 

Alcohol,  C2H5OH 

08-220 

04534 

Regnault. 

53 

I-I33 

Jaeger. 

"             " 

— 

— 

_ 

100 

I-I34 

Stevens, 

«'       C2H8OH 
Ammonia 

01-223 
23-100 

0.4580 
0.5202 

Regnault. 
Wiedemann. 

100 
0 

1.256 
I.3I72 

Wullner. 

"   t        .        .        . 

27-2OO 

0-5356 

" 

100 

1.2770 

« 

"    . 

24-216 

°-5I25 

Regnault. 

Argon   .... 

20-90 

0.1233 

Dittenberger. 

0 

1.667 

Niemeyer. 

Benzole,  C6H6      . 

34-115 

0.2990 

Wiedemann. 

20 

1.403 

Pagliani. 

«            «( 
(i            « 

35-180 

16-218 

0-3325 
0-3754 

a 

Regnault 

60 

99-7 

1.403 
I.IO5 

« 
Stevens 

Bromine 

83-228 

0-0555 

« 

20-388 

1.293 

Strecker. 

"      . 

19-388 

0.0553 

Strecker. 

Carbon  dioxide,  CO2    . 

28-  +7 

0.1843 

Regnault. 

4-1  1 

1.2995 

Lummer  and 

<i           «           i< 

15-100 

0.2025 

it 

Pringsheim. 

«           «           «« 

11-214 

0.2169 

H 

"      monoxide,  CO  ! 

23-99 

0.2425 

Wiedemann. 

0 

1.403 

Wullner. 

<t             ««            « 

26-198 

0.2426 

«< 

IOO 

1-395 

« 

"       disulphide,  CS2 

86-190 

0.1596 

Regnault. 

3-67 

1.205 

Beyme. 

Chlorine 

13-202 

0.1241 

« 

20-340 

!-323 

Strecker. 

"     . 

J6-343 

0.1125 

Strecker. 

o 

1.336 

Martini. 

Chloroform,  CHClg      . 

27-118 

0.1441 

Wiedemann. 

22-78 

1.  102 

Beyme. 

««                « 

28-189 

0.1489 

» 

99.8 

1.150 

Stevens. 

Ether,  C4H100      !        '. 

69-224 

0.4797 

Regnault. 

3-46 

1.025 

Beyme. 

"            " 

27-189 

0.4618 

Wiedemann. 

42-45 

1.029 

Miiller. 

<«            « 

25-111 

0.4280 

<( 

12-20 

1.024 

Low. 

Hydrochloric  acid|  HCi 

13-100 

0.1940 

Strecker. 

2O 

1.389 

Strecker. 

«             <«        « 

22-214 

0.1867 

Regnault. 

IOO 

1.400 

" 

Hydrogen 

28-H-9 

3.3996 

«« 

4-l6 

1.4080 

Lummer  and 

"     . 

12-198 

3.4090 

H 

Pringsheim. 

"     . 

2I-IOO 

3.4100 

Wiedemann. 

"       sulphide,  H2S 

20-206 

0.2451 

Regnault. 

10-40 

1.276 

Miiller. 

Methane,  CH4      . 

18-208 

0.5929 

«« 

II-3O 

1.316 

«« 

Nitrogen 

O-2OO 

0.2438 

• 

- 

1.41 

Cazin. 

"    . 

2O-44O 

0.2419 

Holborn  and 

"    . 

20-630 

0.2464 

Austin. 

«    .        .        .        . 

2O-8OO 

0.2497 

<« 

Nitric  oxide,  NO  . 

13-172 

0.2317 

Regnault. 

Nitrogen  tetroxide,  NO2 

27-67 

1.625 

Berthelot  and 

- 

1.31 

Natanson. 

«              «           « 

27-150 

1.115 

Olger. 

«              «           « 

27-250 

0.65 

» 

Nitrous  oxide,  N2O 

16-207 

0.2262 

Regnault. 

0 

1.311 

Wullner. 

«           «         « 

26-103 

0.2126 

Wiedemann. 

IOO 

1.272 

« 

t<           ««         «i 

27-206 

0.2241 

Oxygen. 

13-207 

0.2175 

Regnault. 

5-14 

1-3977 

Lummer  and 

«      .        .        .        . 

20-440 

0.2240 

Holborn  and 

Pringsheim. 

"      . 

20-630 

0.2300 

Austin. 

Sulphur  dioxide,  SO2    . 
Water  vapor,  H2O 

16-202 

o 

0.1544 
0.4655 

Regnault. 
Thiesen. 

l*# 

1.256 

1.274 

Miiller. 
Beyme. 

«                  t«                 t« 

100 

0.421 

« 

94 

!-33 

Jaeger. 

«                  «                 «( 

180 

0.51 

<« 

SMITHSONIAN  TABLES. 


TABLES  233-236. 
THERMOMETERS. 

TABLE  233. -Gas  and  Mercury  Thermometers. 


233 


If  /H,  to,  Ax>2>  'ie»  *59»  fr,  are  temperatures  measured  with  the  hydrogen,  nitrogen,  carbonic  acid, 
mt  59m,  and  "  verre  dur  "  (Tonnelot),  respectively,  then 

/H  _  tT  =  [—  0.61859  +  0.004735I./—  o.oocoi  1  577-^]* 


/002_  /,  = 


—  4,9 


--0.5554I  +  0.0048240./-0.000024807./2]* 
[—  0.33386  -|-  0.00399IO./—  0.00001  6678.^]* 
[—  0.67039  +  0.004735I./  —  0.00001  1  577./2]t 
[—  0.31089  -f-o.0047351./  —  0.00001  1  S77.^]t 


*  Chappuis  ;  Trav.  et  Me"m.  du  Bur.  internal,  des  Poids  et  Mes.  6,  1888. 

t  Thiesen,  Scheel,  Sell;  Wiss.  Abh.  d.  Phys.  Techn.  Reichanstalt,  2,  1895  ;  Schcel;  Wied.  Ann.  58,  1896;  D.  Mech. 
Ztg.  1897- 

TABLE  234.    tH  —  116   (Hydrogen—  16m). 


0° 

1° 

a° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

0° 
IO 

20 

.000° 

-.056 

—•093 

-.007° 
—.061 
—.096 

-o63° 
—.'098 

—  .019° 
-.069 
—  .IOI 

-.025° 

—.073 
—.103 

-.031° 
—.077 
—  .105 

—.036° 

—.080 
—.107 

-.042° 
-.084 
—.109 

—047° 
-.087 
—  .no 

~.05I° 
—.090 
—  .112 

3° 

—•"3 

—.114 

—•"5 

—.Il6 

—.117 

—  .1  18 

—  .119 

—.119 

—.119 

—  .120 

40 

—  .120 

—  .120 

—  .120 

—  .120 

—.119 

—.119 

—  .Il8 

—.Il8 

—.117 

—.Il6 

£ 

—.116 
—.103 

—•"5 

—  .101 

—.114 

—.099 

—•"3 

—.097 

—  .Ill 
-.096 

—  .no 

—.094 

—.109 
—.092 

—.107 
—.090 

—.106 
-.087 

—.104 
-.085 

£ 

—.083 
—.058 

—.081 
—  .056 

—.078 
—•053 

—  .076 
—  .050 

—.074 
—.048 

—.071 

—.045 

-.069 
—  .042 

—.066 
—.039 

—  .064 
—  .036 

—.O6l 
—•033 

90 

—.030 

—.027 

.024 

—  .021 

—.018 

—.015 

—  .OI2 

—.009 

—.006 

—.003 

100 

.000 

TABLE  235.    fa-lsa    (Hydrogen- 59in). 


0° 

i° 

a° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

0° 

.000° 

—003° 

—.006° 

-.009° 

—.011° 

-.014° 

—.016° 

—.018° 

—  .020° 

—.022° 

IO 
20 
30 

—.024 

—.035 
—.038 

-.025 
—  -036 

—•037 

-.027 
—.036 
—.037 

—.028 
—.037 
—.037 

—.030 
—.037 
—•037 

—.031 

—037 
—.036 

—.032 
—.038 
—.036 

—  03< 

—•034 
—.038 

—035 

—•033 
—.038 

—.034 

40 

—.034 

—033 

—.032 

—.032 

—.031 

—.030 

—  .029 

—.028 

—.028 

—.027 

50 

—  .026 

—.025 

—.024 

—.023 

—  .022 

—  .021 

—  .020 

—  .019 

—.018 

—.017 

60 

—  .016 

—.015 

—.015 

—  .014 

—.013 

—  .OI2 

—  .on 

—  .010 

—.009 

—.008 

£ 

—.008 

—  .001 

—.007 
—  .001 

—.006 
.000 

—.005 
.OOO 

-.005 
+.001 

-.004 

+  .001 

-.003 

+  .001 

-.003 

+  .002 

—  .OO2 
+.002 

—  .OOI 
+  .002 

90 

-f-.002 

-f-002 

+.002 

+.002 

+.002 

+.002 

+.001 

+.001 

+.001 

.000 

100 

.000 

TABLE  236.    (Hydrogen  -  16m),  (Hydrogen  -69"1). 


-5° 

-10° 

-15° 

—20° 

-*5° 

-30° 

-35° 

tH  —  tie 
tH  —  169 

+0.04° 

+0.02° 

+0.08° 

+0.04° 

+0.13° 

+0.07° 

+  0.19° 

+0.10° 

+0.25° 

+0.14° 

+0.320 

+0.18° 

+0.40° 
+0.23° 

All  compiled  from  Landolt-Bornstein-Meyerhoffer's  Physikalisch-chemische  Tabellen. 
SMITHSONIAN  TABLES. 


234 


TABLES  237,  238. 
AIR  AND  MERCURY  THERMOMETERS. 

TABLE  237.    tAm-t16.    (Air-IB1".) 


•C. 

0° 

* 

,o 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

0 

.000 

—.006 

—  .012 

—  .OI7 

—  .022 

—.027 

—  .032 

—•037 

.041 

—.045 

10 

—.049 

—053 

—.057 

—.O6l 

—  .065 

—.068 

—.071 

—.074 

—.077 

—.080 

20 

-.083 

—.086 

—.089 

—.091 

—•093 

—  '°9S 

—.097 

—.099 

—  .101 

—  .IO2 

30 

—.103 

—.104 

-.105 

—.106 

—.107 

—  .108 

—.109 

—  .110 

—  .110 

—  .110 

40 

—  .110 

—  .110 

—  .Ill 

—  .Ill 

—  .110 

—  .110 

—  .110 

—.109 

—.109 

—.I08 

5° 

—.107 

—.107 

—.106 

—.105 

—.104 

—  .103 

—  .102 

—  .101 

—  .IOO 

-.098 

60 
70 

-.096 

—.078 

-.095 

—  .076 

—.093 
—.074 

—.092 
—.072 

—.090 
—  .070 

-.067 

—.086 
-.065 

—.084 
—.062 

—.082 
—.060 

—.080 
—.057 

80 

—.054 

—.052 

—.049 

—.047 

—.044 

—  .041 

—•039 

—  .036 

—.034 

—.031 

90 

—.028 

—.025 

—.023 

—  .020 

—.017 

—.014 

—  .Oil 

—.009 

—.006 

—.003 

IOO 

.000 

+.003 

+.006 

+.008 

+  .011 

+.014 

+.017 

+.019 

+.022 

+  .025 

1  10 

120 

+.028 

+'°53 

+.030 
+•055 

+.033 
+.057 

+-°35 
+.060 

+.038 
+.062 

+.041 
+.064 

+•043 
+.066 

+.046 
+.068 

+  .048 
+.070 

+  •050 
+.072 

130 

+.074 

+.076 

+.078 

+.080 

+.081 

+•083 

+.084 

+.086 

+.087 

+  .089 

140 

+.090 
+.098 

+.091 
+.098 

+.092 
+.098 

+•093 
+.099 

+.094 
+.099 

+•095 
+.099 

+.096 
+.098 

+.096 
+.098 

+.097 

+  .097 

170 

+.097 
+.084 

£82 

+.095 
+.080 

+.094 
+.078 

+•093 
+.076 

+.092 
+•073 

+.090 
+.071 

+.089 
+.068 

+.065 

+!o62 

180 

+.059 

+•055 

+.052 

+.048 

+•045 

+.041 

+.037 

+•033 

+.028 

+.023 

190 

+.019 

+.014 

+.009 

+.004 

—  .001 

—.007 

—.013 

—  .019 

—.025 

—.031 

200 

—.038 

—•045 

—051 

—.058 

—.066 

—•073 

—.080 

—.088 

-.096 

-.105 

210 
22O 

—  [208 

—  .122 

—.130 
—.230 

—  -'39 
—.241 

—.148 

—.252 

-[264 

—.168 
—.275 

—.177 

-.287 

-.187 
—.300 

—.198 
—.312 

230 

—  .325 

—  .338 

—  -351 

—365 

-.378 

—•392 

—.407 

—.421 

-.436 

—.45° 

240 

—  .466 

—  .481 

—•497 

—•529 

—546 

-.562 

—•579 

—597 

-.614 

250 

—  .632 

—  .650 

—.668 

-!687 

-.706 

—.725 

—•745 

—765 

—•785 

-.805 

260 

-.823 

—.846 

-.867 

-.889 

—.911 

—933 

—•955 

-.978 

—  I.OOI 

—  1.025 

270 

—  1.048 

—1.072 

—  1.096 

—  1.  121 

—  1.146 

—1.171 

—  1.196 

—  1.222 

—1.248 

—1.274 

280 
290 

—  1.301 
—1.588 

—1.328 

—  1.618 

—I-356 
—1.649 

-!.68o 

—1.412 
—1.711 

—1.440 
—1-743 

—1.469 
-1.776 

—  1.498 

—  1.808 

—1.528 
—1.841 

-1.558 

—1.874 

300 

—1.908 

TABLE  238.   bin -fa.    (Ail-59"'.) 


°c. 

o« 

1° 

»° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

IOO 

.OOO 

.000 

.OOO 

.OOO 

.OOO 

.000 

.000 

.000 

.000 

.000 

IIO 

.000 

.000 

.000 

—  .001 

—  .OOI 

—.OOI 

—  .OOI 

—  .OOI 

—  .002 

—  .002 

120 

—  .002 

—  .002 

—  .002 

—  .002 

—  .002 

—.003 

—  .003 

—.003 

—.004 

—  .004 

I30 

—  .004 

—.004 

—.005 

—.005 

—.006 

—.006 

—.006 

—.007 

—.007 

—.008 

140 

—.008 

—.008 

—.009 

—.009 

—  .OIO 

—  .OIO 

—  .Oil 

—  .on 

—  .012 

—  .012 

I|° 

—.013 

—.013 

—  .014 

—.015 

—  .Ol6 

—  .016 

—  .016 

—.017 

—.018 

—  .019 

160 

—  .019 

—  .O2O 

—  .021 

—  .021 

—  .022 

—.023 

—  .024 

—.025 

—  .026 

—.027 

170 

—.028 

—  .029 

—.030 

—.031 

—.032 

—•033 

—.034 

—.034 

—.037 

—.038 

1  80 
190 

—039 
-.052 

—  .040 
—.053 

—.041 
-•055 

—.043 
—  .056 

—.044 
—.057 

—.045 
—•059 

—  .046 

—.060 

—  °f 

—.062 

—  °49 
—  .064 

—  .0151 

-.066- 

200 

—.067 

SMITHSONIAN  TABLES. 


TABLES  239-241 .  235 

GAS,   MERCURY,   ALCOHOL,   TOLUOL,    PETROLETHER,   PENTANE,  AND 
PLATINUM-RESISTANCE  THERMOMETERS. 

TABLE  239.    t^— tu  (Hydrogen-Mercury). 


Temper- 
ature, C. 

Thuringer 
Glass> 

Verre  dur. 
Tonnelott 

Resistance 
Glass* 

English 
Crystal 
Glass* 

Choisy-le- 
RoL* 

,,,m. 

Nitrogen 
Thermometer. 
TH-TN.t 

CO2  Ther- 
mometer. 
TH—  TCo2.t 

o 

0 

o 

0 

0 

0 

o 

o 

o 

O 

.000 

.000 

.OOO 

.OOO 

.000 

.000 

.OOO 

.000 

IO 

—075 

—.052 

—.066 

—.008 

—.007 

—.005 

—.006 

—.025 

20 

—.125 

-.085 

—.108 

—  .OOI 

—.004 

—  .006 

—  .010 

—.043 

30 
40 

-.156 
-.168 

—  .102 

—.107 

—  .140 

+.017 
+•037 

+.004 
+.014 

—  .002 

-f.ooi 

—  .Oil 
—  .Oil 

—.054 
—.059 

£ 

—.166 

-rsija 

—.103 
—.090 

—  135 
—.119 

+  .057 
+.073 

+.025 
+•033 

+.004 
+  .008 

—.009 

—.005 

—.059 
—.053 

70 

—.124 

—.072 

—  -°95 

+  -079 

+.037 

+  .009 

—  .OOI 

—.044 

80 

—.088 

—  .050 

—  .068 

+  .070 

+.032 

+  .007 

+  .002 

—.031 

90 

—.047 

—  .026 

—.034 

+.046 

-f  -022 

+.006 

+  .003 

—  .016 

100 

.000 

.000 

.000 

.000 

.000 

.000 

.OOO 

.000 

*  Schlosser,  Zt.  Instrkde.  ax,  1901. 


t  Chappuis,  Trav.  et  me"m.  du  Bur.  Intern,  des  Poids  et  Mes.  6,  1888. 


TABLE  240  —Comparison  of  Air  and  High  Temperature  Mercury  Thermometers. 

Comparison  of  the  air  thermometer  with  the  high  temperature  mercury  thermometer,  filled  under 

pressure  and  made  of  59m  glass. 


Air. 

59ra- 

Air. 

59ra. 

0 

o 

o 

o 

0 

0. 

375 

3854 

100 

100. 

400 

412.3 

200 

200.4 

425 

44.0*7 

300 

304.1 

450 

469.1 

325 
350 

330-9 
358.1 

475 
500 

527.8 

Mahlke,  Wied.  Ann.  1894. 


TABLE  241.— Comparison  o!  Hydrogen  and  Other  Thermometers. 

Comparison  of  the  hydrogen  thermometer  with  the  toluol,  alcohol,  petrolether,  and  pentane  ther- 
mometers (verre  dur). 


Hydrogen. 

Toluol* 

Alcohol  I* 

Alcohol  II.* 

Petrolether.  t 

Pentane.  J 

0 

0 

o 

o 

0 

0 

0 

O.OO 

0.00 

O.OO 

- 

0.00 

—  10 
—  2O 

-8.54 
—  16.90 

—9-31 
—18.45 

—9-44 
—18.71 

; 

—9-03 
—17.87 

—3° 

—  25.10 

—27.44 

—27.84 

- 

—26.55 

—40 

—5° 

—33-15 
—41.08 

—36.30 

—45-05 

-36.84 
—45-74 

—  42.5 

—35-04 
—43-36 

—60 
—70 

—  IOO 

~^T 
-56.63 

—53.71 

—  62.31 

—54-55 
—63-31 

—80.2 

—  5!-5o 
—59-46 
—82.28 

—150 

- 

- 

- 

—113.0 

—116.87 

—  200 

~ 

" 

—140.7 

—146.84 

*  Chappuis,  Arch.  sc.  phys.  (3)  18,  1892.  t  Holborn,  Ann.  d.  Phys.  (4)  6,  1901.  t  Rothe,  unpublished. 

All  compiled  from  Landolt-Bornstein-Meyerhoffer's  Physikalisch-chemische  Tabellen. 
SMITHSONIAN  TABLES. 


236  TABLE  242. 

CORRECTION  FOR  TEMPERATURE  OF  MERCURY  IN  THERMOMETER 

STEM. 

The  Stem  Correction  is  proportional  to  «/3(  T— /) :  where  n  is  the  number  of  degrees  in  the 
exposed  stem ;  /3  is  the  apparent  coefficient  of  expansion  of  mercury  in  the  glass ;  T  is  the  measured 
temperature ;  and  t  is  the  mean  temperature  of  the  exposed  stem  determined  by  another  ther- 
mometer, exposed  some  10  cm.  from,  and  at  about  half  the  height  of,  the  exposed  stem  of  the  first. 

For  temperatures  up  to  ioo°C,  the  value  of  ft  is  for : 

Jena  glass  XVIra  or  Greiner  and  Friedrich  resistance  glass,  ^—  or  0.000159; 


Jena  glass  59™,  or  0.000164. 


6300 


At  100°  the  correction  is  in  round  numbers  0.01°  for  each  degree  of  the  exposed  stem ;  at  200° 
0.02° ;  and  for  higher  temperatures  proportionately  greater.  At  500°  it  may  amount  to  0.07°  for 
each  exposed  degree. 

Tables  242-244  are  taken  from  Rimbach,  Zeitschrift  fiir  Instrumentenkunde,  10,  153,  1890,  and 
apply  to  thermometers  of  Jena  or  of  resistance  glass. 


TABLE  242. -Stem  Correction  for  Thermometer  of  Jena  Glass  (0°-360°  0.). 

Degree  length  0.9  to  i.i  mm;  /=the  observed  temperature;  /'=that  of  the  surrounding  air 
i  dm.  away ;  n  =  the  length  of  the  exposed  thread. 


CORRECTION  TO  BE  ADDED  TO  THE  READING  t. 

*—  *' 

70° 

80° 

90° 

100° 

120° 

140° 

160° 

180° 

200° 

220° 

10 

0.01 

0.0  1 

0.03 

0.04 

0.07 

O.IO 

0.13 

0.17 

0.19 

0.21 

20 

3° 

0.08 
0.25 

0.12 
0.28 

0.14 
0.32 

0.19 
0.36 

0.25 
0.42 

0.28 
0.48 

0.32 
0-54 

0.40 
0.66 

0.49 
0.78 

0.87 

40 

0.30 

o-35 

0.41 

0.48 

O.6o 

0.67 

0.77 

0.92 

1.  08 

1.20 

£ 
g 

0.41 

0.52 

0.63 

0.75 

0.46 
0.60 
0.74 
0.87 

0.52 
0.68 
0.85 

1.  01 

o-59 
0.79 
0.98 

1.  1C 

0.79 
0.99 

1.20 

0.89 
I.  II 

1.32 

!-53 

0.98 
1.23 

1-45 
1.70 

1.16 
1.46 
1.70 
1.98 

1.38 
1.70 
1.99 
2.29 

'•53 

1.87 

2.21 
2-54 

90 

0.87 

0.99 

1-13 

1.28 

1.62 

1.82 

1.94 

1.25 

2.60 

2.89 

100 

0.98 

1.  12 

1.29 

1.47 

1.82 

2.03 

2.20 

2-55 

2.92 

3-24 

120 

- 

- 

1.88 

2.28 

2.49 

2.68 

3-i3 

3-59 

3.96 

140 

- 

- 

- 

- 

2-75 

2.97 

3.22 

3-75 

4.24 

4.69 

160 

— 

— 

— 

— 

3-35 

3.80 

4-35 

4.92 

5-45 

180 

200 

— 

• 

— 

— 

"• 

4.37 

4-99 
5.68 

6.34 

6.22 
6.98 

2  2O 

" 

" 

7-oS 

7.82 

SMITHSONIAN  TABLES. 


237 

THERMOMETER 


TABLES  243,  244. 
CORRECTION   FOR   TEMPERATURE   OF   MERCURY   IN 

STEM    (continued). 

TABLE  243. -Stem  Correction  lor  Thermometer  of  Jena  Glass  (0°-360°  0). 

Degree  length  i  to  1.6  mm.;  /=the  observed  temperature;  /=that  of  the  surrounding  air 
one  dm.  away ;  n  =  the  length  of  the  exposed  thread. 


CORRECTION  TO  BE  ADDED  TO  THERMOMETER  READING.* 

t—v 

70° 

80° 

90° 

100° 

120° 

140° 

160° 

180° 

200° 

220° 

10° 

0.02 

0.03 

0.05 

0.07 

O.I  I 

0.17 

O.2I 

0.27 

0-33 

0.38 

10° 

20 

0.13 

o.is 

0.18 

0.22 

O.29 

0.38 

0.46 

0-53 

0.6  1 

0.67 

20 

3° 

0.24 

0.28 

0.33 

0-39 

0.48 

o-59 

0.70 

0.78 

0.88 

0.97 

30 

40 

°-35 

0.41 

0.48 

0.56 

0.68 

0.82 

0.94 

1.04 

1.16 

1.28 

40 

50 

0.47 

0-53 

0.62 

0.72 

0.88 

1.03 

I.I7 

j.3I 

1.44 

i-59 

50 

60 

g 

0.69 
0.80 

0.66 
0.79 
0.91 

0.77 
0.92 
1.05 

0.89 
1.  06 
1.  21 

1.09 
1.30 
1.52 

1.25 
1.47 
1.71 

1.42 
1.67 
1.94 

1.86 
2.15 

1.74 
2.04 
2-33 

1.90 
2.23 
2-55 

60 

£ 

90 

0.91 

1.04 

1.19 

1.38 

i-73 

1.96 

2.20 

2.42 

2.64 

2.89 

90 

100 

1.02 

1.18 

1.35 

I.56 

1.97 

2.18 

2-45 

2.70 

2.94 

3-23 

100 

no 
1  20 

- 

- 

- 

I.78 
1.98 

2.19 
2.43 

2-43 
2.69 

2.70 
2-95 

2.98 
3.26 

3.26 
3-58 

3-57 
3-92 

no 
1  20 

130 

- 

_ 

_ 

_ 

2.68 

2.94 

3.20 

3-56 

3-89 

4.28 

130 

140 

- 

- 

-    -. 

- 

2.92 

3.22 

347 

3-86 

4.22 

4.64 

140 

X 

- 

- 

- 

- 

- 

- 

3-74 
4.00 

4.46 

4.90 

5.01 
5-39 

'g 

160 

170 

1  80 

- 

- 

- 

- 

- 

- 

4.27 
4-54 

4.76 

5-24 
5-59 

5-77 
6-15 

170 

180 

190 

200 

- 

: 

: 

- 

- 

- 

5-70 

£95 
6.30 

6.54 
6.94 

190 

200 

210 

_ 

~ 

_ 

- 

- 

- 

- 

- 

6.68 

7-35 

210 

220 

7.04 

775 

220 

*  See  Hovestadt's  "  Jena  Glass"  (translated  by  J.  D.  and  A.  Everett)  for  data  on  changes  of  thermometer  zeros. 

TABLE  244.  —  Stem  Correction  for  a  so-called  Normal  Thermometer  of  Jena  Glass  (0°  100°  0). 
Divided  into  tenth  degrees ;  degree  length  about  4  mm. 


CORRECTION  TO  BE  ADDED  TO  THK  READING  f. 

t—v 

30° 

35° 

40° 

45° 

60° 

65° 

60° 

65° 

70° 

76° 

80° 

86° 

10. 

0.04 

0.04 

0.05 

0.05 

0.05 

0.06 

0.06 

0.07 

0.08 

0.09 

O.IO 

O.IO 

20 

0.12 

0.12 

0.13 

0.14 

0.15 

0.16 

0.17 

0.18 

0.19 

0.20 

0.22 

0.23 

30 

0.21 

0.22 

0-23 

0.24 

0.25 

0.25 

0.27 

0.29 

0.31 

°-33 

0-35 

0.37 

40 

g 

0.28u 
0.36 
0-45 

0.29 
0.38 
0.48 

0.31 
0.40 
0.51 

o-33 
0.42 

0-53 

0-35 
0.44 

o-55 

0-37 
0.46 

0-39 
0.48 
0.60 

0.41 
0.50 
0.63 

043 
°-53 
0.66 

045 
0.69 

0.48 

0.61 
o.73 

0.51 

0.65 

0.78 

£ 

_ 

~ 

0.66 

0.69 
0.76 

0.71 
0.8  1 

0-75 
0.87 

0.8  1 
0-93 

0.87 

1.  00 

0.92 

1.  06 

90 

— 

— 

— 

— 

— 

— 

— 

0.92 

0.99 

i.  06 

I-I3 

1.20 

IOO 

" 

" 

" 

~ 

" 

" 

1.  10 

1.18 

1.26 

1-34 

SMITHSONIAN  TABLES. 


238  TABLES  245-247. 

RADIATION  CONSTANTS. 
TABLE  245.  —  Radiation  Formula  and  Constants  for  Perfect  Radiator. 

The  radiation  per  sq.  cm.  from  a  "  black  body  "  (exclusive  of  convection  losses)  at  the  temper- 
ature T°  (absolute,  C)  to  one  at  /°  is  equal  to 

/=  ff  (  T*  —  /*)     (Stefan-Boltzmann)  ; 

where  <t=  i.277Xio~12  gramme-calories  per  second  per  sq.  centimetre. 
=  7.66  X  lo-11        "  «         «    minute    "    « 

=  5.32  X  io~12  watts  per  sq.  centimetre. 
The  distribution  of  this  energy  in  the  spectrum  is  represented  by  Planck's  formula  : 


where  /A  is  the  intensity  of  the  energy  at  the  wave-length  X  (X  expressed  in  microns,  ju)  and  e  is 
the  base  of  the  Napierian  logarithms.  From  Kurlbaum's  value  of  the  difference  of  the  total 
energy  radiated  from  black  bodies  at  100°  C  and  o°  C,/ioo  —  /o  =  0.0731  watts  per  square  cen- 
timetre (whence  the  above  value  of  a)  and  \auaT==2g^o  (the  mean  of  Paschen's  and  Lummer's 
values),  the  following  constants  have  been  calculated  (see  Planck,  Ann.  d.  Phys.  4,  p.  562,  1901)  : 

Ci  =  8.813  X  io8  for/  in 
C2  =  14550  for  X  in  microns 
/max  =  2.869  X  io~16  T5  for/in 
Xm«7'=  2930  for  X  in  microns  (ft) 


=  *-200  X  io-167'&  for/in 


TABLE  246.  —  Radiation  in  Gramme- Calories  per  24  Hours  from  a  Perfect  Radiator  at  «°  0  to  an  abso- 
lutely Cold  Space  (-273°  0). 
Computed  from  the  Stefan-Boltzmann  formula  (Ekholm,  Met.  Z  1902). 


*°c 

/ 

*°C 

/ 

*°C 

/ 

*°c 

/ 

*°C 

/ 

t°c 

/ 

—273 

o 

—  1  20 

60 

—  IO 

528 

+  12 

728 

+34 

980 

+  S6 

1292 

—  22O 

I 

—  no 

78 

—8 

544 

+  14 

748 

+36 

1006 

I324 

—  210 

2 

—  100 

99 

—6 

56i 

+  16 

769 

fSB 

1032 

+60 

!356 

—  200 

3 

—90 

124 

—  4 

S78 

+  18 

791 

+4o 

1050, 

+70 

!53° 

—100 

—  180 

—80 
—70 

$ 

—  2 
0 

595 
613 

+  20 
+  22 

8« 

836 

+42 
+44 

1114 

+80 
+90 

1713 
1916 

—170 

12 

—60 

227 

+  2 

631 

+  24 

8S9 

+46 

1142 

+  IOO 

2134 

—  160 

18 

—50 

273 

+4 

+  26 

882 

+48 

1171 

+  200 

55r9 

—150 

25 

—40 

324 

+6 

668 

+  28 

906 

+  50 

1  201 

-|-IOOO 

290X108 

—140 

35 

—30 

38S 

+8 

688 

+30 

93° 

+  S2 

1231 

-J-2OOO 

294X10* 

—130 

46 

—  20 

452 

+  10 

708 

+32 

955 

+54 

I26l 

+5000 

852XI05 

TABLE  247.  — Values  of  JA  for  Various  Temperatures  Centigrade. 

Ekholm,  Met.  Z.  1902,  used  Ci  =  8346  X  io  and  C2  =  14349,  and  for  the  unit  of  time  the  day. 
For  10°,  the  values  for  J\  have  been  multiplied  by  io,  for  the  other  temperatures  by  100. 


x 

T=^C 

30°  C 

15°  C 

o°C 

—  30°  C 

—  80°  C 

x 

100°  C 

30°  C 

15°  C 

ooc 

—  30°  C 

-So°C 

2 

3 

4 

I 

80 
409 

O 

£ 

0 

18 

272 

0 

J 

o 
i 

27 

O 
0 

M 

18 

19 

20 

5" 

443 

2961 

2626 
2329 

2557 
2281 
2034 

2175 
1954 
1754 

1491 

1363 
1242 

623 

594 

1 

1047 
1526 

'777 
3464 

1085 

628 
'4S4 

172 

493 

8 
39 

21 
22 

337 
29$ 

2068 

1840 

1816 
1622 

1574 

1129 
1026 

527 
494 

7 

1768 

49S4 

3481 

2353 

I05 

23 

2S9 

1639 

1448 

1270 

93  * 

460 

8 

1810 

S928 

4352 

3088 

1372 

203 

24 

228 

1462 

1298 

II4I 

846 

428, 

9 

10 

ii 

1724 
1308 

6382 
6386 
6127 

4834 
4979 
4833 

3646 
378i 
3798 

1730 
1971 
2098 

426 

520 

11 

28 

202 
179 
142 

1307 

1170 
947 

1165 
1047 
850 

1028 
926 

757 

768 
698 
579 

317 

12 

1225 

^712 

4633 

3676 

2114 

592 

30 

114 

771 

696 

623 

482 

272 

13 

1063 

5222 

4300 

3467 

2090 

640 

40 

44 

3»J 

285 

259 

209 

130 

H 

918 

4713 

3930 

3215 

2004 

666 

So 

20 

146 

'35 

124 

1  02 

67 

15 

792 

4220 

3556 

2944 

1889 

673 

00 

10 

77 

72 

66 

55 

38 

i6 

683 

3759 

3198 

2674 

1760 

663 

80 

4 

27 

2S 

24 

20 

1*4 

17 

590 

3340 

2862 

2417 

1626 

649 

100 

2 

12 

II 

10 

9 

7 

SMITHSONIAN  TABLES. 


TABLES  248,  249. 
COOLING  BY  RADIATION  AND  CONVECTION. 


239 


TABLE  248.  —  At  Ordinary  Pressures. 

According  to  McFarlane*  the  rate  of  loss  of  heat  by  a  sphere 
placed  in  the  centre  of  a  spherical  enclosure  which  has  a 
blackened  surface,  and  is  kept  at  a  constant  temperature  of 
about  14°  C,  can  be  expressed  by  the  equations 


e  =  .000138  +  3.06  X  10-6*  _  2.6  X 
when  the  surface  of  the  sphere  is  blackened,  or 
e  =  .000168  +  1.98  X  io—  *t  —  1.7  X 


when  the  surface  is  that  of  polished  copper.  In  these  equa- 
tions, e  is  the  amount  of  heat  lost  in  c.  g.  s.  units,  that  is, 
the  quantity  of  heat,  small  calories,  radiated  per  second  per 
square  centimetre  of  surface  of  the  sphere,  per  degree  differ- 
ence of  temperature  /,  and  t  is  the  difference  of  temperature 
between  the  sphere  and  the  enclosure.  The  medium  through 
which  the  heat  passed  was  moist  air.  The  following  table 
gives  the  results. 


Differ- 
ence of 
tempera- 
ture 
t 

Value  of  e. 

Ratio. 

Polished  surface. 

Blackened  surface. 

5 

.000178 

.O00252 

.707 

10 

.000186 

.O00266 

.699 

IS 

.000193 

.000279 

.692 

20 

.OOO2OI 

.000289 

.695 

25 

.000207 

.000298 

.694 

30 

.000212 

.000306 

.693 

35 

.000217 

.000313 

•693 

40 

.OOO22O 

.000319 

•693 

45 

.000223 

.000323 

.690 

50 

.000225 

.000326 

.690 

55- 

.000226 

.000328 

.690 

60 

.OOO226 

.000328 

.690 

TABLE  249.  —  At  Different  Pressures. 

Experiments  made  by  J.  P.  Nicol  in  Tail's  Labo- 
ratory show  the  effect  of  pressure  of  .the  en- 
closed air  on  the  rate  of  loss  of  heat.  In  this 
case  the  air  was  dry  and  the  enclosure  kept  at 
about  8»  C. 


Polished  surface. 

Blackened  surface. 

t 

et 

t 

et 

PRESSURE  76  CMS.  OF  MERCURY. 

63.8 

.00987 

6T.2 

.01746 

57-1 
50-5 
44.8 

.00862 
.00736 
.00628 

50.2 
41.6 

34-4 

.01360 
.01078 
.00860 

40-5 

.00562 

27-3 

.00640 

34-2 
29.6 

.00438 
.00378 

20.5 

.00455 

23.3 

.00278 

- 

- 

18.6 

.00210 

" 

" 

PRESSURE  10.2  CMS.  OF  MERCURY. 

67.8 

.00492 

62.5 

.01298 

61.1 

•00433 

57-5 

.01158 

55 

.00383 

53-2 

.01048 

497 

.00340 

47-5 

.00898 

44-9 

.00302 

43.0 

.00791 

40.8 

.00268 

28.5 

.00490 

PRESSURE  i  CM.  OF  MERCURY. 

65 

.ooiSS 

62.5 

.01182 

00 

-ooSs 

57-5 

.01074 

50 

.00286 

54-2 

.01003 

40 

.00219 

41.7 

.00726 

30 

.00157 

37-5 

.00639 

23-5 

.00124 

34-o 

.00569 

- 

- 

27.5 

.00446 

24.2 

.00391 

SMITHSONIAN  TABLES. 


*  "  Proc.  Roy.  Soc."  1872. 
t  "  P.roc.  Roy.  Soc."  Edinb.  1869. 
See  also  Compan,  Annal.  de  chi.  et  phys.  26,  p.  526. 


240  TABLES  250,  251 . 

COOLING  BY  RADIATION  AND  CONVECTION. 

TABLE  250.  — Cooling  of  Platinum  Wire  In  Copper  Envelope. 

Bottomley  gives  for  the  radiation  of  a  bright  platinum  wire  to  a  copper  envelope  when  the  space  between  is  at  the 
highest  vacuum  attainable  the  following  numbers :  — 

*  =  4o8°  C.,  <rf  =  378.8  X  10-*,  temperature  of  enclosure  16°  C. 

/=  505°  C.,  et—  726. i  X  io-*,          "  "          17°  C. 

It  was  found  at  this  degree  of  exhaustion  that  considerable  relative  change  of  the  vacuum  produced  very  small 
change  of  the  radiating  power.  The  curve  of  relation  between  degree  of  vacuum  and  radiation  becomes  asymp- 
totic for  high  exhaustions.  The  following  table  illustrates  the  variation  of  radiation  with  pressure  of  air  in 
enclosure. 


Temp,  of  enclosure  16°  C.,  *=:4o8°  C. 

Temp,  of  enclosure  17°  C.,  t=.  505°  C. 

Pressure  in  mm. 

et 

Pressure  in  mm. 

et 

740. 

8137.0  X  io-* 

0.094 

1688.0  X  lo-4 

440. 
140. 

7971.0    " 
7875.0    « 

•053 
•034 

1255.0    " 
1126.0    " 

42. 

7591.0    ' 

.013 

920.4    " 

4- 

6036.0    " 

.0046 

83M    " 

0.444 

2683.0    « 

.00052 

767.4    " 

.070 

1045.0    " 

.00019 

746.4    " 

•034 
.012 

727.3    « 
539-2    " 

Lowest  reached    ) 
but  not  measured  ) 

726.1     « 

.0051 

436.4    " 

.OOOO7 

378.8    « 

TABLE  251. —Effect  of  Pressure  on  Loss  of  Heat  at  Different  Temperatures. 

The  temperature  of  the  enclosure  was  about  15°  C.    The  numbers  give  the  total  radiation  in  therms  per  square 

timetre  per  second. 


Pressure  in  mm. 

Temp,  iji 

wire  in  &. 

About 

IO.O 

I.O 

0.25 

0.025 

o.i  M. 

100° 

0.14 

O.I  I 

0.05 

O.OI 

0.005 

200 

•31 

.24 

.11 

.02 

•°°55 

300 

•50 

.38 

.18 

.04 

.0105 

400 

•75 

•53 

•25 

.07 

.025 

|00 

— 

.69 

•33 

•13 

•055 

600 

— 

.85 

•45 

•23 

•13 

700 

— 

•37 

.24 

800 

_ 

_ 

_ 

.56 

.40 

900 

— 

— 

— 

.61 

NOTE.  —  An  interesting  example  (because  of  its  practical  importance  in  electric  light- 

ing) of  the  effect  of  difference  of  surface  condition  on  the  radiation  of  heat  is  given  on  the 

authority  of  Mr.  Evans  and  himself  in  Bottomley's  paper.     The  energy  required  to  keep 

up  a  certain  degree  of  incandescence  in  a  lamp  when  the  filament  is  dull  black  and  when 

it  is  "  flashed  "  with  coating  of  hard  bright  carbon,  was  found  to  be  as  follows  :  — 

Dull  black  filament,  57.9  watts. 

Bright  "           "        39.8  watts. 

SMITHSONIAN  TABLES. 


TABLE  252. 
PROPERTIES  OF  STEAM. 

Metric  Measure. 


241 


The  temperature  Centigrade  and  the  absolute  temperature  in  degrees  Centigrade,  tqgetherVith  other  data  for  steam 
or  water  vapor  stated  in  the  headings  of  the  columns,  are  here  given.  The  quantities  of  heat  are  in  therms  or  calo- 
ries according  as  the  gramme  or  the  kilogramme  is  taken  as  the  unit  of  mass. 


u 

I 

Absolute  temp..  >  1 

Pressure  in  mm.  1 
of  mercury. 

Pressure  in 
grammes  per  sq. 
centimetre  =/. 

.32 

§1 

£1 

Total  heat  of  evap-  1 
oration  from  o°  at  1 
t°  —  H,  .-.  | 

*3 
.2* 

w?l 

Heat  of  evapora-  1 
tion  =  #•—£«  ,/ 

Outer  latent  or  ex-  1 
ternal-work  heat 
—  Apv,*  \ 

Total  heat  of 
steam  —H—Afv.  \ 

Inner  latent  or  in-  1 
ternal-work  heat 
=H-(h  +  Atv).  \ 

Litres  per  gramme, 
or  cubic  metres 
per  kilog.  =  v. 

Ratio  of  inner  la- 
tent heat  to  vol- 
ume of  steam.  f 

0° 

5 

273 

278 

4.60 
6-53 

8.88 

0.006 
.009 

606.5 
6o8.0 

0.00 

5.00 

606.5 
603.0 

31.07 

3M7 

575-4 
576.5 

575-4 

21O.66 
150.23 

2.732 

10 

283 

9.17 

12.47 

.012 

609.5 

IO.OO 

599-5 

31.89 

567-7 

108.51 

5-23I 

i5 

20 

288 
293 

12.70 
17-39 

17.27 
23.64 

.017 
.023 

611.1 
612.6 

15.00 

20.01 

596.0 
592.6 

32.32 
32.75 

§Si 

579-8 

563-7 
559-8 

7.9-35 
78.72 

7.104 
9-532 

25 

298 

23-55 

32.02 

0.031 

614.1 

25.02 

589.1 

33-20 

580.9 

555-9 

43-96 

12.64 

30 

303 

3L55 

42.89 

.042 

615.6 

30.03 

585.6 

33-66 

582.0 

552.0 

33-27 

16.59 

35 

308 

41.83 

56.87 

.055 

617.2 

35-04 

582.1 

34.12 

583-1 

548.2 

25-44 

21.54 

40 

3J3 

54-91 

74.65 

.072 

618.7 

40.05 

587-6 

34-59 

584.1 

544-.I 

19.64 

27.70 

45 

3l8 

71-39 

97.06 

.094 

620.2 

45-07 

575-1 

35.06 

585-2 

540.1 

35-26 

50 

323 

91.98 

125.0 

O.I2I 

621.7 

50.09 

sll'7 

35-54 

586.2 

536.1 

12.049 

44-49 

g 

333 

117.47 
148.79 

159.7 

202.3 

•'55 
.196 

623.3 
624.8 

5S-" 
60.13 

568.2 
5647 

36.02 
36-51 

588.3 

532-1 
528.1 

9.561 
7-653 

55-65 
69.02 

65 

338 

186.94 

254.2 

.246 

626.3 

65-17 

561.1 

37.00 

589.3 

524.2 

6.171 

84.94 

70 

343 

233.08 

316.9 

.306 

627.8 

70.20 

557-6 

3748 

590-4 

520.2 

5.014 

103-75 

8 

348 
353 

288.50 
354-62 

392.3 

482.1 

0.380 
__.446 

629.4 
630.9 

75-24 
80.28 

554-1 
550-6 

37-96 
38.42 

591-4 
592.5 

516.2 
512.2 

4.102 
3-379 

125.8 
151.6 

85 

358 

433-oo 

588.7- 

632.4 

85-33 

547-1 

38-88( 

>593-5 

508.2 

2.800 

181.5 

90 

363 

525-39 

714.4 

.691 

633-9 

90.38 

543-6 

39-33 

594-6 

504.2 

2-334 

216.0 

95 

368 

633-69 

861.7 

•834 

635-5 

95-44 

540.0 

39-76 

595-7 

500.3 

1-957 

255-7 

100 

373 

760.00 

1033- 

1.  000 

637.0 

100.5 

536.5 

40.20 

596.8 

496-3 

1.6496 

300.8 

105 

378 

906.41 

1232. 

.193 

638-5 

105.6 

533-o 

40-63 

597-9 

492.3 

1.3978 

352.2 

no 
"5 

388 

1075-4 
1269.4 

1462. 

1726. 

.415 

.670 

640.0 
641.6 

uo.6 
"5-7 

529-4 
525.8 

41.05 
41.46 

599-o 
600.  i 

488.4 
484.4 

1.1903 
1.0184 

410.3 
475-6 

I2O 

393 

I49I-3 

2027. 

.962 

643.1 

120.8 

522-3 

41.86 

601.2 

480.4 

0.8752 

549.0 

"5 

130 

135 

140 

398 
403 
408 

1743-9 
2030.3 

2353-7 
2717.6 

2760. 
3200. 
3695- 

2.295 

2.671 

3-097 
3-576 

644-6 
646.1 

6477 
649.2 

125.9 
131.0 
136.1 
141.2 

518-7 

511.6 

508.0 

42.25 
42.63 
43.01 
43-38 

602.4 

603-5 
604.7 
605.8 

472-5 
468.6 
464.6 

0-7555 
0.6548 
0.5698 
0.4977 

630.7 
721.6 
822.3 
933-5 

J3 

3I25-6 

4249. 

4.113 

650.7 

146.3 

504.4 

43-73 

607.0 

460.7 

04363 

1055-7 

150 

423 

3581.2 

4869. 

4.712 

652.2 

151.5 

500.8 

44.09 

608.2 

456.7 

0.3839 

1190. 

J55 

428 

4088.6 

5-380 

653.8 

'56-5 

497-2 

44-43 

609.3 

452.8 

0.3388 

I336- 

160 
165 

433 
438 

4651.6 
5274-5 

6324. 
7171. 

6.120 

6.940 

655-3 
656.8 

161.7 
166.9 

493-5 
489.9 

44.76 
45.09 

610.5 
611.7 

448.8 
444-8 

0.3001 
0.2665 

1496. 
1669. 

170 

443 

8105. 

7.844 

658.3 

172.0 

486.3 

45.40 

612.9 

440.9 

0-2375 

1856. 

i 

448 
453 
458 

6717.4 
7546.4 
8453-2 

9J33- 
10260. 
11490. 

8.839 
9.929 
11.123 

659.9 
661.4 
662.9 

177.2 
182.4 
187.6 

482,7 
479-o 
475-3 

45-71 
46.01 
46.30 

N  Tj-\O 

•<i-uo\d 

\OvS\S 

436.9 
433-o 
429.0 

0:2122 
0.1901 
0.1708 

2059. 
2277. 
2512. 

190 

463 

9442-7 

12838. 

12.425 

664.4 

192.8 

471-7 

46.59 

617.9 

425.0 

0.1538 

2763. 

195 

468 

10520. 

14303- 

13.842 

666.0 

198.0 

468.0 

46.86 

619.1 

421.1 

0.1389 

3031' 

200 

473 

11689. 

15892. 

15.380 

667.5 

203.2 

464-3 

47.13 

620.4 

417.1 

0.1257 

33.8- 

*  Where  A  is  the  reciprocal  of  the  mechanical  equivalent  of  the  thermal  unit. 


f  - 


_        internal-work  pressure 


Where  y  {&  uken  ^  Utreg  ^  pressure  is 


_ 

v  mechanical  equivalent  of  heat 

decimetre,  and  where  v  is  taken  in  cubic  metres  the  pressure  is  given  per  square  metre,  —  the  mechanical  equivalent 
being  that  of  the  therm  and  the  kilogramme-degree  or  calorie  respectively. 

SMITHSONIAN  TABLES. 


242 


TABLE  253. 
PROPERTIES  OF  STEAM. 

British  Measure, 


The  quantities  given  in  the  different  columns  of  this  table  are  sufficiently  explained  by  the  headings.  The  abbrevia- 
tion B.  T.  U.  stands  for  British  thermal  units.  With  the  exception  of  column  3,  which  was  calculated  for  this 
table,  the  data  are  taken  from  a  table  given  by  Dwelshauvers-Dery  (Trans.  Am.  Soc.  Mech.  Eng.  vol.  xi.). 


Pressure 
in  pounds  per 
square  inch. 

Pressure 
in  pounds  per  1 
square  foot. 

Pressure  in 
atmospheres. 

4 

djj 

II 

S3 
p 

III 

Weight  per 
cubic  foot  in 
pounds. 

!'!. 

Internal  latent  I 
heat  per  pound  1 
of  steam  in 
B.  T.  U.  1 

External  latent  I 
heat  per  pound  1 
of  steam  in 
B.  T.  U. 

Total  latent 
heat  per  pound  I 
of  steam  in 
B.  T.  U.  1 

1 

1 

144 

0.068 

IO2.O 

334.23 

0.0030 

70.1 

980.6 

62.34 

1043. 

1113.0 

2 

288 

.136 

126.3 

/'  73-23 

.0058 

94.4 

961.4 

64.62 

IO26. 

1  1  20.4 

3 

432 

.204 

141.$ 

117.98 

.0085 

109.9 

949-2 

66.58 

IOII. 

1127.0 

4 

576 

.272 

I53-1 

89.80 

.0111 

121.4 

940.2 

67.06 

1007. 

1128.6 

5 

720 

•340 

162.3 

72.50 

•0137 

130.7 

932-8 

67.89 

1001. 

1131.4 

6 

864 

0.408 

170.1 

61.10 

0.0163 

138-6 

926.7 

68.58 

995.2 

"33-8 

7 

1008 

476 

176.9 

53-00 

.0189 

145-4 

921.3 

69.18 

"35-9 

8 
9 

IIS2 
1296 

•544 
.012 

182.9 
188.3 

46.60 
41.82 

.0214 
.0239 

151.5 
156.9 

916.5 
912.2 

69.71 
70.18 

982.4 

"37-7 
"39-4 

10 

1440 

.680 

193.2 

37.80 

.0264 

161.9 

908.3 

70.61 

979-0 

1140.9 

11 

1584 

0.748 

197.8 

34.61 

0.0289 

166.5 

904.8 

70.99 

975-8 

1142.3 

12 

1728 

.8l6 

202.0 

31.90 

.0314 

170.7 

901.5 

71-34 

972.8 

"43-5 

13 

1872 

.884 

205.9 

29-58 

.0338 

174.7 

898.4 

71.68 

970.0 

1144.7 

14 
15 

20l6 
2l6o 

•952 
1.020 

209.5 
213.0 

27-59 
25-87 

:°387 

178.4 
181.9 

895.4 
892.7 

72.00 
72.29 

967.4 
965-0 

"45-9 
1146.9 

16 

2304 
2448 

1.088 
.156 

2l6.3 
219.4 

24-33 
22.98 

0.0411 

.0435 

185.2 
188.4 

890.1 
887.6 

72-57 
72.g2 

962.7 
960.4 

1147.9 
1148.9 

18 
19 

2592 
2736 

.224 
.292 

222.4 
225.2 

21.78 
20.70 

•0459 
.0483 

191.4 
194-3 

885.3 
883.1 

73-07 
73-30 

958.3 
956.3 

1149.8 
1  1  50.6 

20 

2880 

.360 

227.9  ' 

19.72 

.0507 

197.0 

880.9 

73-53 

9544 

1151.4 

21 

3024 

1.429 

230.5 

18.84 

0.0531 

199.7 

878.8 

73-74 

952-6 

1152.2 

22 

3168 

497 

233.0 

18.03 

.0554 

202.2 

876.8 

73-94 

950.8 

"53-o 

23 

3312 

.565 

2354 

17-30 

.0578 

204.7 

874.9 

74-13 

949.1 

"53-7 

24 

3456 

•633 

2377 

16.62 

.0602 

2O7.O 

873.1 

74.32 

947-4 

"54-4 

25 

3600 

.701 

24O.O 

iS-99 

.0625 

209.3 

871-3 

74-51 

945-8 

"55-1 

26 

3744 

1.769 

242.2 

15.42 

0.0649 

2II.5 

869.6 

74.69 

944-3 

"55-8 

27 

3888 

244-3 

14.88 

.0672 

213.7 

867.9 

74.85 

942.8 

1156.4 

28 

4032 

•9"5 

246.3 

14.38 

.0695 

215-7 

866.3 

75-oi 

941-3 

"57-i 

29 

4176 

•973 

248.3 

13.91 

.0619 

217.8 

864.7 

75-17 

939-9 

"57-7 

30 

4320 

2.041 

250.2 

13.48 

.0742 

219.7 

863.2 

75-33 

938-5 

"58-3 

31 

4464 

2.109 

252.1 

13-07 

0.0765 

221.6 

861.7 

75-47 

937-2 

1158.8 

32 

4608 

.177 

253-9 

12.68 

.0788 

223-5 

860.3 

75-6i 

935-9 

"59-4 

33 

4752 

•245 

255-7 

12.32 

.0811 

225-3 

858.9 

7576 

934-6 

"59-9 

34 

35 

5040 

$1 

257-5 
259.2 

11.98 
11.66 

.0835 
.0858 

227.1 
228.8 

857-5 
856.1 

75.89 
76.02 

933-4 
932.1 

1160.5 
1161.0 

36 

5^4 

2.449 

260.8 

11.36 

0.0881 

230.5 

854.8 

76.16 

931.0 

1161.5 

37 

5328 

•5J7 

262.5 

11.07 

.0903 

232.2 

853-5 

76.28 

929.8 

1162.0 

38 

5472 

.585 

264.0 

10.79 

.0926 

233-8 

852.3 

76.40 

928.7 

1162.5 

39 

5616 

•653 

265.6 

10.53 

.0949 

235-4 

851.0 

76.52 

927.6 

1162.9 

40 

5760 

.722 

267.1 

10.29 

.0972 

236.9 

849.8 

76.63 

926.5 

1163.4 

41 

5904 

2.789 

268.6 

10.05 

0.0993 

238.5 

848.7 

76.75 

9254 

1163.9 

42 

6048 

•857 

270.1 

9-83 

.1018 

239-9 

847.5 

76.86 

924.4 

1164.3 

43 

6192 

.925 

271.5 

9.61 

.1040 

241.4 

846.4 

76.97 

923-3 

1164.7 

44 

6336 

•993 

272.9 

9.41 

.1063 

242.9 

845.2 

77.07 

922.3 

1165.2 

45 

6480 

3.061 

274-3 

9.21 

.1086 

244-3 

844.1 

77.18 

921.3 

1165.6 

46 

6624 

3.129 

275.6 

9.02 

0.1108 

245-6 

843-1 

77.29 

920.4 

1166.0 

48 

6768 
6912 

.197 
.265 

277.0 
278.3 

8.84 
8.67 

.1131 
•"53 

247.0 
248.3 

842.0 
841.0 

77-39 
77-49 

919.4 
918.5 

1166.4 
1166.8 

49 

7056 

•333 

279.6 

8.50 

.1176 

249.7 

840.0 

77-58 

9I7.5 

1167.2 

SMITHSONIAN  TABLE*. 


TABLE  253  (conti*u*d\ 
PROPERTIES   OF  STEAM. 

British  Measure. 


243 


Pressure  in 
pounds  per 
square  inch. 

Pressure  in 
pounds  per 
square  foot. 

Pressure  in 
atmospheres. 

Temp,  in 
degrees  Fahr. 

Volume  per 
pound  in 
cubic  feet. 

Weight  per 
cubic  foot 
in  pounds. 

Heat  of  water 
per  pound  in 
B.  T.  U. 

Internal  latent 
heat  per  pound 
of  steam  in 
B.  T.  U. 

External  latent  1 
heat  per  pound  1 
of  steam  m 
B.  T.  U. 

ik 

Total  heat  per 
pound  of  steam 
m  B.  T.  U. 

50 

7200 

3.401 

280.8 

8-34 

0.1198 

251.0 

839.0 

77.67 

916.6 

1167.6 

5i 

7344 

.469 

282.1 

8.19 

.1221 

252.2 

838.0 

77.76 

9*5-7 

1168.0 

53 

7488 
7632 

•537 
.605 

283-3 
284.5 

8.04 
7.90 

'.1266 

253.5 
2547 

837.0 
836.0 

'    '       Q 

77*"5 
77-94 

914.9 
914.0 

1168.3 
1168.7 

54 

7776 

•673 

2857 

7.76 

.1288 

256.0 

835.I 

78-03 

9I3-1 

1169.1 

55 

7920 

3741 

286.9 

7.63 

O.I3IO 

257.I 

834-2 

78.12 

912.3 

1169.4 

56 

8064 

.801 

288.1 

7.50 

•I333 

258.3 

833.2 

78.21 

1169.8 

8208 

.878 

289.2 

7-38 

•!355 

259.5 

832.3 

78.29 

910.6 

1170.1 

59 

8352 
8496 

.946 
4.014 

290.3 
291.4 

7.26 
7.14 

•1377 
.1400 

260.7 
261.8 

830.6 

78.37 
78.45 

909.8 
909.0 

1170.5 
1170.8 

60 

61 

8640 
8784 

4.082 
.150 

292.5 
293.6 

7-03 

0.1422 
.1444 

262.9 
264.0 

829.7 
828.9 

78.53 
78.61 

908.2 
907-5 

1171.2 
II7I.5 

62 
63 

8928 
9072 

.218 
.286 

2947 
295-7 

672 

.1466 
.1488 

265.1 
266.1 

828.0 
827.2 

78.68 
7876 

906.7 
905-9 

1171.8 
1172.1 

64 

9216 

•354 

296.7 

6.62 

.15" 

267.2 

826.4 

78-83 

905.2 

1172.4 

65 

9360 

4.422 

297.8 

6.52 

o-i533 

268.3 

825-6 

78.90 

904.5 

1172.8 

66 

9504 

.490 

298.8 

6-43 

•1555 

269.3 

824.8 

78.97 

9037 

1173.1 

67 

9648 

•558 

299.8 

6-34 

•1577 

270.4 

824.0 

79-04 

903.1 

"73-4 

68 
69 

9792 
9936 

.626 
.694 

300.1 
301.8 

6.25 
6.17 

•1599 
.1621 

271.4 
272.4 

823.2 
822.4 

79.11 
79.18 

902.3 
901.6 

"73-7 
1174.0 

70 

10080 

4.762 

302.7 

6.09 

0.1643 

273-4 

821.6 

79-25 

900.9 

"74-3 

71 

10224 

.830 

3037 

6.00 

.1665 

274-3 

820.9 

79-32 

900.2 

1174.6 

72 
73 

10368 
10512 

.898 
.966 

304.6 
3°5-5 

5-93 
5.85 

.1687 
.1709 

275-3 
276.3 

820.1 

79-39 
79-46 

899-5 

1174.9 
H75-1 

74 

10656 

5.034 

306.5 

5.78 

•I73I 

277.2 

818.7 

79-53 

898.1 

"75-4 

75 

10800 

5.102 

3074 

5-70 

0.1753 

278.2 

817.9 

79-59 

897.5 

"75-7 

76 

77 
78 

10944 
11088 
11232 

.170 
.238 
.306 

308.3 
309.2 
310.1 

5-63 
5-57 
5-50 

•1775 
.1797 
.1818 

279.1 
280.0 
280.9 

817.2 
816.5 
815.8 

79-65 
79.71 

79-77 

896.9 
896.2 
895.6 

1176.0 
1176.2 
1176.3 

79 

11376 

•374 

310.9 

5-43 

.1840 

281.8 

815.1 

79-83 

895-0 

1176.8 

80 

11520 

5-442 

3II.8 

5-37 

0.1862 

282.7 

8144 

79.89 

894.3 

1177.0 

81 
82 
83 

11664 
11808 
11952 

.510 
•578 
.646 

312.7 
3I3-5 
3H-4 

5-31 
5-25 
5-J9 

.1884 
.1906 
.1928 

283.6 
284.5 
285-3 

813.8 
813.0 
812.4 

79-95 
80.01 
80.07 

893-7 
893.1 
892.5 

"77-3 
1177.6 
1177.8 

84 

12096 

.714 

3I5-2 

5-^3 

.1949 

286.2 

811.7 

80.13 

891.9 

1178.0 

85 

86 

12240 
11384 

5.782 
.850 

316.0 
316.8 

5-07 
5-02 

0.1971 

287.0 
287.9 

8x1.1 

810.4 

80.19 
80.25 

891.3 
890.7 

1178.3 
1178.6 

87 
88 

12528 
12672 

.918 
.986 

317.6 
318.4 

4-96 
4.91 

.2015 
.2036 

288.7 
289.5 

809.8 

80.30 
80.35 

1178.9 
1179.0 

89 

12816 

6.054 

319.2 

4.86 

.2058 

290.4 

808.5 

80.40 

888.9 

"79-3 

90 

12960 

6.122 

320.0 

4.81 

0.2080 

291.2 

807.9 

80.45 

888.4 

"79-5 

91 

13104 

.190 

320.8 

4-76 

.2102 

292.0 

807.3 

80.50 

887.8 

1179-8 

92 

13248 

.258 

321.6 

4.71 

.2123 

292.8 

806.7 

80.56 

887.2 

1180.0 

93 

I3392 

•327 

322.4 

4.66 

.2145 

293.6 

806.1 

80.61 

886.7 

1180.3 

94 

13536 

•396 

323-1 

4.62 

.2166 

294-3 

805.5 

80.66 

886.1 

1180.5 

95 

13680 

6.463 

323-9 

4.57 

0.2188 

295.1 

804.9 

80.71 

885.6 

1180.7 

96 

13824 

•531 

324.6 

.2209 

295-9 

804.3 

80.76 

885.0 

1180.9 

97 

13968 

•599 

3254 

4.48 

.2231 

296.7 

8037 

80.8  1 

884.5 

1181.2 

98 

14112 

.667 

326.1 

4-44 

.2252 

297.4 

803.1 

80.86 

884.0 

1181.4 

99 

14256 

•735 

326.8 

4.40 

.2274 

298.2 

802.5 

80.91 

883.4 

1181.6 

SMITHSONIAN  TABLES. 


244 


TABLE  253  (continued). 
PROPERTIES  OF  STEAM. 

British  Measure. 


Pressure  in 
pounds  per 
square  inch. 

Pressuie  in 
pounds  per 
square  foot. 

Pressure  in 
atmospheres. 

J 

*""*    CO 

Volume  per 
pound  in 
cubic  feet. 

Weight  per 
cubic  foot  in 
pounds. 

Heat  of  water 
per  pound  in 

b.T.  u. 

Internal  latent 
heat  per  pound  I 
of  steam  in 
B.  T.  U. 

External  latent  1 
heat  per  pound  1 
of  steam  in 
B.  T.  U. 

g  1-2 

Ml* 

^  +*  ~EH 

us* 

Total  heat  per 
pound  of  steam  I 
in  B.  T.  U. 

100 

14400 

6.803 

327.6 

4-356 

0.2295 

298.9 

802.0 

80.95 

882.9 

1181.8 

101 

14544 

.871 

328.3 

.316 

.2317 

299-7 

801.4 

81.00 

882.4 

II82.I 

IO2 

I4688 

•939 

329.0 

.276 

.2338 

300.4 

800.8 

81.05 

881.9 

1182.3 

103 

14832 

7.007 

329-7 

.237 

.2360 

301.1 

800.3 

81.10 

881.4 

1182.5 

104 

14976 

.075 

3304 

.199 

•2381 

301.9 

799-7 

81.14 

880.8 

1182.7 

105 

I5I20 

7-143 

331-! 

4.161 

0.2403 

302.6 

799-2 

81.18 

880.3 

1182.9 

!    106 

15264 

.211 

331.8 

.I2C 

.2424 

303.3 

798.6 

81.23 

879.8 

1183.1 

107 

15408 

•279 

332.5 

.088 

.2446 

304.0 

798.1 

81.27 

879.3 

1183.4 

108 

'5552 

•347 

333-2 

•053 

.2467 

304.7 

797-5 

81.31 

878.8 

1183.6 

109 

15696 

415 

333-8 

.018 

.2489 

305-4 

797-o 

81.36 

878.3 

1183.8 

110 

15840 

7483 

334-5 

3-984 

0.2510 

306.1 

796.5 

81.41 

877.9 

1184.0 

in 

15984 

.551 

335-2 

•950 

.2531 

306.8 

795-9 

81.45 

8774 

1184.2 

112 

16128 

.619 

335-8 

.917 

•2553 

307.5 

7954 

81.50 

876.9 

1184.4 

"3 

16272 

.687 

336.5 

.885 

.2574 

308.2 

794-9 

81.54 

876.4 

1184.6 

114 

16416 

•757 

337-2 

•853 

.2596 

308.8 

7944 

8158 

875.9 

1184.8 

115 

16560 

7.823 

337-8 

3.821 

0.2617 

309.5 

793-8 

81.62 

875.5 

1185.0 

116 

16704 

.891 

338.5 

.790 

.2638 

310.2 

793-3 

81.66 

875.0 

1185.2 

117 

16848 

•959 

339-  i 

.760 

.2660 

310.8 

792.8 

81.70 

874.5 

1185.4 

118 

16992 

8.027 

339-7 

•73° 

.2681 

3".5 

792.3 

81.74 

874.1 

1185.6 

119 

17*36 

•095 

3404 

.700 

.2702 

312.1 

791.8 

81.78 

873.6 

1185.7 

120 

17280 

8.163 

341.0 

3.671 

0.2724 

312.8 

791-3 

81.82 

873.2 

1185.9 

121 

17424 

.231 

341.6 

•643 

.2745 

3134 

790.8 

81.86 

872.7 

II86.I 

122 

17568 

•299 

342.2 

.615 

.2766 

3I4-i 

790.3 

81.90 

872.2 

1186.3 

123 

17712 

•367 

342-8 

•587 

.2787 

3M-7 

789.9 

81.94 

871.8 

1186.5 

124 

17856 

435 

343-5 

.560 

.2809 

315-3 

789.4 

81.98 

871.4 

1186.7 

125 

18000 

8.503 

344-1 

3-534 

0.2830 

316.0 

788.9 

82.02 

870.9 

1186.9 

126 

18144 

•571 

344-7 

•507 

.2851 

316.6 

788.4 

82.06 

870.5 

1187.1 

127 

18288 

.639 

345-3 

.481 

.2872 

317.2 

787.9 

82.09 

870.0 

1187.2 

128 

18432 

.708 

345-9 

456 

.2893 

3I7-8 

787-5 

82.13 

869.6 

1187.4 

129 

18576 

.776 

346.5 

431 

.2915 

318.4 

787.0 

82.17 

869.2 

1187.6 

130 

18720 

8.844 

347-1 

3.406 

0.2936 

319.0 

786.5 

82.21 

868.7 

1187.8 

132 

18864 
19008 

.912 
.980 

347-6 
348.2 

.382 
•358 

-2957 
.2978 

3I9-7 
320.3 

786.1 
785-6 

82.25 
82.28 

868.3 

867.9 

II88.0 
II88.I 

19152 

9.048 

348.8 

•334 

•2999 

320.9 

785.1 

82.32 

867.5 

1188.3 

134 

19296 

.116 

349-4 

.310 

.3021 

32L5 

7847 

82.35 

867.0 

1188.5 

135 

19440 

9.184 

349-9 

3.287 

0.3042 

322.1 

784.2 

82.38 

866.6 

Il88.7 

136 

19584 

.252 

350-5 

.265 

.3063 

322.6 

783.8 

82.42 

866.2 

II88.8 

137 

19728 

.320 

424 

.3084 

323-2 

783-3 

82.45 

865.8 

1189.0 

138 

19872 

•388 

351-6 

.220 

.3105 

323-8 

782.9 

82.49 

865.4 

1189.2 

139 

20016 

456 

352.2 

.199 

.3126 

3244 

782.4 

82.52 

865.0 

1189.4 

140 

20160 

9-524 

352-8 

3.177 

0.3147 

325-0 

782.0 

82.56 

864.6 

1189.5 

141 
142 
143 

20304 
20448 
20592 

•592 
.660 

.728 

353-3 
353-9 
3544 

.156 
•135 

.3168 
.3190 
.3211 

325.5 
326.1 
326.7 

781.6 
781.1 
780.7 

82.59 
82.63 
82.66 

864.2 
863.8 
863.4 

1189.7 
1189.9 
1190.0 

144 

20736 

.796 

355-o 

.094 

.3232 

327.2 

780.3 

82.69 

863.0 

1190.2 

145 

20880 

9.864 

355-5 

3-074 

0.3253 

327.8 

779-8 

82.72 

862.6 

1190.4 

146 

21024 

•932 

.054 

.3274 

328.4 

7794 

82.75 

862.2 

1190.5 

147 

21168 

10.000 

3S&6 

•035 

.3295 

328-9 

779-0 

82.79 

861.8 

1190.7 

148 

21312 

.068 

357-1 

.016 

778.6 

82.82 

861.4 

1190.9 

149 

21456 

.136 

357-6 

•997 

•3337 

330-o 

778.1 

82.86 

861.0 

1191.0 

SMITHSONIAN  TABLES, 


TABLE  253  (continued). 
PROPERTIES  OF  STEAM. 

British  Measure. 


245 


Pressure  in 
pounds  per 
square  inch. 

Pressure  in 
pounds  per 
square  foot. 

Pressure  in 
atmospheres. 

J 

AJj 

II 

Volume  per 
pound  in 
cubic  feet. 

Weight  per 
cubic  foot  in 
pounds. 

Heat  of  water 
per  pound  in 
B.  T.  U.  1 

Internal  latent 
heat  per  pound  1 
of  steam  in 
B.  T.  U. 

External  latent  I 
heat  per  pound  1 
of  steam  in 
B.  T.  U.  1 

Total  latent 
heat  per  pound 
of  steam  in 
B.  T.  U. 

Total  heat  per 
pound  of  steam  1 
in  B.  T.  U. 

150 

2l6oo 

10.204 

358.2 

2.978 

o.3358 

330-6 

777-7 

82.89 

860.6 

II9I.2 

151 

21744 

.272 

3587 

.960 

•3379 

777-3 

82.92 

860.2 

1191.3 

152 

21888 

•340 

359-2 

.941 

.3400 

33I-6 

776.9 

82.95 

859-9 

1191.5 

153 

154 

22032 
22176 

.408 
476 

359-7 
360.2 

31 

.3421 
•3442 

332-2 
3327 

776.5 
776.1 

82.98 
83.01 

f59.5 
859.1 

II9I.7 
II9I.8 

155 

22320 

10.544 

360.7 

2.888 

0.3462 

333-2 

775-7 

83-04 

858.7 

II92.O 

156 

22464 

.6l2 

361.3 

.871 

•3483 

333-8 

775-3 

83.07 

858.3 

II92.I 

157 

22608 

.680 

361-8 

.854 

•35°4 

334-3 

774-9 

83.10 

858.0 

1192.3 

159 

22752 
22896 

.748 
.816 

362.3 
362.8 

•837 
.820 

•3525 
•3546 

334-8 
335-3 

774-5 
774-1 

83-13 
83-16 

857-6 
857.2 

1192.4 
1192.6 

160 

161 

23040 
23184 

10.884 
•952 

363-3 
363-8 

2.803 
•787 

0.3567 

335-9 
336.4 

773-7 
773-3 

83.19 
83.22 

856.9 
856.5 

1192.7 
1192.9 

162 

23328 

11.020 

364-3 

.771 

.3609 

336.9 

772.9 

83-25 

856.1 

1193.0 

163 

23472 

.088 

364-8 

•755 

•3630 

337-4 

772-5 

83-28 

855.8 

1193.2 

164 

23616 

•157 

365-3 

•739 

•3650 

337-9 

772.1 

83-3I 

855-4 

"93-3 

165 

23760 

11.225 

365.7 

2.724 

0.3671 

338.4 

771.7 

83-34 

855-1 

IJ93-5 

166 

23904 

•293 

366.2 

.708 

.3692 

338.9 

771-3 

83-37 

8547 

1193.6 

167 

24048 

.361 

366.7 

•693 

•3713 

339-4 

771.0 

83-39 

854.3 

1193.8 

168 

24192 

.429 

367.2 

.678 

•3734 

339-9 

770.6 

83.42 

854.0 

11  93-9 

169 

24336 

•497 

367-7 

•663 

•3754 

340-4 

770.2 

8345 

853.6 

1194.1 

170 

171 

24480 
24624 

"•565 
•633 

368.2 
368.6 

2.649 
•634 

0-3775 
•3796 

340.9 
341-4 

769.8 
769-4 

8348 
83-5I 

852^9 

1194.2 
1194.4 

172 

24768 

.701 

369.1 

.620 

•3817 

341-9 

769.1 

83-54 

852.6 

"94-5 

173 

24912 

.769 

369-6 

.606 

•3838 

342.4 

768.7 

83.56 

852.2 

1194.7 

174 

25056 

•837 

370.0 

•592 

.3858 

342.9 

768.3 

83-59 

851.9 

1194.8 

175 

25200 

11.905 

370.5 

2.578 

0.3879 

343-4 

767.9 

83.62 

851.6 

1194.9 

176 

25344 

•973 

371.0 

•564 

.3900 

343-9 

767.6 

83.64 

851.2 

1195.1 

177 

25488 

12.041 

371-4 

•550 

.3921 

344-3 

767.2 

83.67 

850.9 

1195.2 

178 

25632 

.109 

371-9 

•537 

•3942 

344-8 

766.8 

83.70 

850.5 

II95-4 

179 

25776 

.177 

372.4 

524 

•3962 

345-3 

766.5 

83-73 

850.2 

"95-5 

180 

25920 

12.245 

372.8 

2.510 

0-3983 

345-8 

766.1 

8375 

849.9 

1195.6 

181 

26064 

•313 

373-3 

•497 

.4004 

346.3 

765-8 

8377 

849-5 

1195.8 

182 

26208 

.381 

373-7 

.485 

.4025 

346.7 

765-4 

83.80 

849-2 

"95-9 

183 

26352 

•449 

374-2 

•472 

.4046 

347-2 

765.0 

83.83 

848.9 

1196.1 

184 

26496 

374-6 

•459 

.4066 

347-7 

764.7 

83.86 

848.5 

1196.2 

185 

186 
187 

26640 
26784 
26928 

12.585 
•653 
.721 

375-1 
375-5 
376.0 

2.447 

•434 
.422 

0.4087 
.4108 
.4129 

348.1 
348.6 

349-  x 

764-3 
764-0 
763-6 

83.88 
83-90 
83-92 

848.2 
847.9 

1196.3 
1196.5 
1196.6 

188 

27072 

.789 

.410 

.4150 

349-5 

763-3 

83.95 

847^2 

1196.7 

189 

27216 

.857 

376.8 

•398 

.4170 

350-0 

762.9 

83.97 

846.9 

1196.9 

190 

27360 

12.925 

377-3 

2.386 

0.4191 

3504 

762.6 

83.99 

846.6 

1197.0 

191 
192 

27504 
27648 

•993 
13.061 

377-7 
378.2 

•374 
.362 

.4212 
•4233 

350-9 
351-3 

762.2 
761-9 

84.02 
84.04 

846.3 
845-9 

1197.1 
"97-3 

193 

27792 

.129 

378.6 

•35' 

•4254 

351-8 

761.6 

84.06 

845-6 

1197.4 

194 

27936 

.197 

379-o 

•339 

•4275 

352.2 

761.2 

84.08 

845-3 

"97-5 

195 

28080 

13-265 

379-4 

2.328 

0.4296 

352-7 

760.9 

84.10 

845.0 

1197.7 

196 

28224 

•333 

379-9 

•3*7 

.4316 

353-1 

760.5 

84.13 

844.7 

1197.8 

197 

28368 

.401 

380.3 

•306 

•4337 

353-6 

760.2 

84.16 

844.4 

1197.9 

199 

28512 
28656 

•469 
•537 

380.7 
381-1 

'III 

•4358 
•4379 

354-o 
354-4 

759-9 
759-5 

84.19 
84.21 

844.0 
843.7 

1198.1 
1198.2 

SMITHSONIAN  TABLES. 


246 


TABLE  253  (continued). 
PROPERTIES  OF  STEAM. 

British  Measure. 


Pressure  in 
pounds  per 
square  inch. 

Pressure  in 
pounds  per 
square  foot. 

es  8 

Temp,  in 
degrees  Fahr. 

Volume  per 
pound  in 
cubic  feet. 

Weight  per 
cubic  foot  in 
pounds. 

ii 

Internal  latest 
heat  per  pound 
of  steam  in 
B.  T.  U. 

External  latent  1 
heat  per  pound  1 
of  steam  in 
B.  T.  U. 

jl 

HE 

Total  heat  per 
pound  of  steam  1 
in  B.  T.  U. 

200 

2OI 

28800 
28944 

13605 

381.6 
382.0 

2.273 
.262 

0.4399 
.4420 

354.9 
355.3 

759-2 
758.9 

84.23 
84.26 

843-4 
843.1 

1198.3 
1198.4 

2O2 

29088 

I3742 

3824 

.252 

.4441 

355.8 

758.5 

84.28 

842.8 

1198.6 

203 
204 

29232 
29376 

13.810 
13-878 

382.8 

.241 
.231 

.4461 
.4482 

356.2 
356.6 

758.2 
757-9 

84.30 
84.33 

842.5 
842.2 

1198.7 
1198.8 

205 

29520 

13.946 

3837 

2.221 

0.4503 

357.1 

757-5 

84.35 

841.9 

II99.0 

206 

29664 

14.014 

384.1 

.211 

-4523 

357.5 

757-2 

84.37 

841.6 

1199.1 

207 

29808 

14.082 

384.5 

.201 

•4544 

357.9 

84.40 

841.3 

1199.2 

208 
209 

29952 
30096 

14.150 
14.218 

384.9 

.191 

.4564 
.4585 

gs 

756$ 
756-2 

8442 
84.44 

841.0 
840.7 

"99-3 
1199.4 

210 

30240 

14.386 

3857 

2.I7I 

0.4605 

359-2 

755-9 

84.46 

840.4 

1199.6 

211 

30384 

14454 

386.1 

.162 

.4626 

359-6 

755-6 

84.48 

840.1 

1199.7 

212 

30528 

14.522 

386.5 

.152 

.4646 

360.0 

755-3 

84.51 

839.8 

1199.8 

213 

30672 

386.9 

.143 

.4666 

360.4 

755-o 

84.53 

839-5 

1199.9 

214 

30816 

14.658 

387.3 

•134 

.4687 

360.9 

754-7 

84.55 

839.2 

1200.1 

215 

216 

30960 
31104 

14.726 
14-794 

3877 
388.1 

2.124 

0.4707 
.4727 

361-3 
361.7 

754-3 
754-o 

its 

838.9 

1200.2 
1200-3 

217 

31248 

14.862 

388.5 

.IO6 

.4748 

362.1 

753-7 

84.62 

838.3 

I2OO.4 

218 

3r392 

14.930 

388.9 

.097 

.4768 

362.5 

753-4 

84.64 

838.0 

I2OO-5 

219 

14.998 

.088 

.4788 

362.9 

753-1 

84.66 

837-7 

1200-7 

SMITHSONIAN  TABLES. 


TABLE  254. 


247 


RATIO  OF  THE    ELECTROSTATIC  TO  THE   ELECTROMAGNETIC  UNIT 

ELECTRICITY  =  F- 


OF 


Date. 

V 
Cm.  per  sec. 

Mean. 

Determined  by 

Reference. 

1856 

3-iiXio10 

R.  Kohlrausch  and 

W.  Weber. 

Pogg.  Ann.  99  ;  1856. 

1868 

2.75-2.92  X  io10 

2.84 

Maxwell. 

Phil.  Trans.  ;  1868. 

1869 
1874 

2.71-2.88 
2.86-3.00 

2.8l 
2.90 

Thomson  and  King. 
McKichan. 

B.  A.  Report  ;  1869. 
Phil.  Mag.  47;  1874. 

1879 
1879 

2.950-3.018 

2.981 
2.96 

Rowland. 
Ayrton  and  Perry. 

Phil.  Mag.  28  ;  1889. 
Phil.  Mag.  7  ;  1879. 

I879 

— 

2.967 

Hockin. 

B.  A.  Report  ;  1879. 

1880 
1881 

2.98-3.00 

2-955 
2.99 

Shida. 
Stoletow. 

Phil.  Mag.  io  ;  1880. 
Jour,  de  Phys.  ;  1881. 

1882 

__ 

2.87 

Exner. 

Wien.  Ber.  ;  1882. 

1883 
1884 

3.001-3.029 

2.963 
3.019 

J.  J.  Thomson. 
Klemencic. 

Phil.  Trans.  ;  1883. 
Wien.  Ber.  83,  89,  93  ;  1881-6. 

« 

3.016-3.031 

1886 

3-°iS 

Colley. 

Wied.  Ann.  28  ;  1886. 

1886-8 

2.999-3-0°9 

« 

3.003-3.008 

3.009 

Himstedt. 

Wied.  Ann.  29,  33,  35  ;  1887-8. 

« 

3.005-3.015 

1888 

2.92 

Thomson,    Ayrton 

and  Perry. 

Electr.  Rev.  23  ;  1888-9. 

1889 

2.995-3.010 

3.000 

Rosa. 

Phil.  Mag.  28  ;  1889. 

1890 

2.996 

J.  J.  Thomson  and 

Searle. 

Phil.  Trans.  ;  1890. 

1891 

- 

3.009 

Pellat. 

Jour,  de  Phys.  io  ;  1891. 

1892 

2.990-2.995 

2.991 

Abraham. 

Ann.  Chim.  et  Phys.  27;  1829. 

1896 

3.001 

Hurmuzescu. 

Ann.  Chim.  et  Phys.  io  ;  1897. 

1898 

— 

2-9973 

Perot  and  Fabry. 

Ann.  Chim.  et  Phys.  13  ;  1898. 

1898 

— 

3.026 

Webster. 

Phys.  Rev.  6  ;  1898. 

1899 

- 

3.009 

Lodge    and    Glaze- 

brook. 

Cam.  Phil.  Soc.  18  ;  1899. 

1904-7 

2.99706-2.99741 

2.9971 

Rosa  and  Dorsey. 

Bull.  Bur.  Standards  3  ;  1907. 

The  last  of  the  above  determinations  is  the  result  of  an  extended  series  of  measurements  upon 
various  forms  of  condensers,  and  is  believed  to  be  correct  within  I  /ico  per  cent.  This,  however, 
assumes  that  the  International  Ohm  is  io9  c.g.s.  units.  The  value  of  V\&  therefore  subject  to 
one-half  the  error  of  the  International  Ohm. 


SMITHSONIAN  TABLES. 


248  TABLES  255,  256. 

DIELECTRIC   STRENGTH. 

TABLE  255.  —  Steady  Potential  Difference  In  Volts  required  to  produce  a  Spark  In  Air  with  Ball  Electrodes. 


Spark 
length, 
cm. 

R  =  o. 
Points. 

R  =  0.25 
cm. 

R  =  0.5 
cm. 

/?=i  cm. 

R  =  a  cm. 

R  =»  3  cm. 

R=K>. 

Plates. 

0.02 

_ 

_ 

1560 

1530 

0.04 

— 

— 

2460 

2430 

2340 

0.06 

— 

— 

3300 

3240 

3060 

0.08 

- 

- 

4050 

3990 

38lO 

O.I 

3720 

COIO 

4740 

4560 

4560 

4500 

4350 

0.2 

4680 

8610 

8490 

8490 

8370 

7770 

7590 

o-3 

5310 

11140 

11460 

11340 

III90 

10560 

10650 

0.4 

5970 

14040 

14310 

H340 

14250 

13140 

13560 

°-5 
0.6 

6300 
6840 

!S990 
17130 

16950 
19740 

17220 
20070 

16650 
20070 

16470 
19380 

16320 
19110 

0.8 

8070 

18960 

23790 

24780 

25830 

26220 

24960 

I.O 

8670 

20670 

26190 

27810 

29850 

32760 

30840 

i-5 

9960 

22770 

29970 

37260 

2.0 

10140 

2&l° 

33060 

45480 

3-o 

11250 

28380 

4.0 

I22IO 

29580 

5-o 

I30SO 

Based  on  the  results  of  Bailie,  Bichat-Blondot,  Freyburg,  Liebig,  Macfarlane,  Orgler,  Paschen,  Quincke,  de  la  Rue, 
Wolff.  For  spark  lengths  from  i  to  200  wave-lengths  of  sodium  light,  see  Earhart,  Phys.  Rev.  15,  p.  163;  Hobbs, 
Phil.  Mag.  10,  p.  607,  1905. 


TABLE  266.— Alternating  Current  Potentials  required  to  produce  a  Spark  In  Air  with  various  Ball  Elec- 
trodes. 

The  potentials  given  are  the  maxima  of  the  alternating  waves  used.    Frequency,  33  cycles  per 

second. 


Spark  length. 
cm. 

J?—i  cm. 

R  =  i.g2 

*  =  5 

*  =  7-5 

/?=IO 

J?  =  iS 

0.08 

3770 

.10 

4400 

4380 

433° 

4290 

4245 

4230 

•IS 

599° 

5940 

5830 

5790 

5800 

5780 

,2O 

75*o 

7440 

7340 

7250 

7320 

7330 

•25 

9045 

8970 

8850 

8710 

8760 

8760 

0.30 

10480 

10400 

10270 

IOI30 

IOl8o 

10150 

•35 

11980 

11890 

11670 

11570 

Il6lO 

II590 

.40 

13360 

13300 

13100 

12930 

12980 

12970 

•45 

14770 

14700 

14400 

14290 

14330 

14320 

•50 

16140 

16070 

15890 

15640 

15690 

15690 

0.6 

18700 

18730 

18550 

18300 

18350 

18400 

•7 

21350 

21380 

21140 

20980 

20990 

2IOOO 

.8 

23820 

24070 

23740 

23490 

23540 

23550 

0.9 

26190 

26640 

26400 

26130 

26lIO 

26090 

1.0 

28380 

29170 

28950 

28770 

28680 

28610 

1.2 

32400 

34100 

33790 

33660 

33640 

33620 

1.4 

35850 

38850 

38850 

38580 

38620 

38580 

1.6 
1.8 

38750 
40900 

43400 

43570 
48300 

43250 
47900 

43520 

2.0 

42950 

52400 

Based  upon  the  results  of  Kawalski,  Phil.  Mag.  18,  1909. 


SMITHSONIAN  TABLES. 


TABLES  257,  258.  249 

DIELECTRIC  STRENGTH. 

TABLE  257.— Potential  Necessary  to  produce  a  Spark  in  Air  between  more  widely  Separated  Electrodes. 


e 

f 

'  Steady  potentials. 

e 

2  . 

<i  s 

Steady  potentials. 

! 

Ball  electrodes. 

Cup  electrodes. 

JS 

a 

i'E 

Ball  electrodes. 

•s 

a.s 

Projection. 

M 

af 

s. 

13  o 

R=i  cm. 

R:-=2.5  cm. 

C/3 

3  o 

R=i  cm. 

R—  j  .5  cm. 

Q 

4.5  mm. 

1.5  mm. 

Q 

0.3 

_ 

_ 

__ 

_ 

II280 

6.0 

6lOOO 

_ 

86830 

- 

17610 

17620 

- 

17420 

7.0 

- 

52000 

- 

0.7 

— 

— 

23050 

— 

22950 

8.0 

67000 

52400 

90200 

1.0 
1.2 

12000 

30240 
33800 

3J390 
36810 

31400 

31200 
36700 

10.0 
12.0 

73000 
82600 

74300 

91930 
93300 

1-5 

— 

37930 

— 

445  10 

14.0 

92000 

— 

94400 

2.0 

292OO 

42320 

56500 

56530 

15.0 

— 

— 

94700 

2-5 

—  • 

45000 

— 

68720 

1  6.0 

IOIOOO 

— 

IOIOOO 

40000 

46710 

71200 

80400 

81140 

2O.O 

119000 

3-5 

— 

— 

75300 

— 

92400 

25.0 

140600 

4.0 

48500 

49100 

78600 

IOI7OO 

103800 

30.0 

165700 

4-5 

— 

— 

81540 

— 

114600 

35-o 

190900 

5-O 

56500 

50310 

83800 

— 

126500 

5-5 

135700 

This  table  for  longer  spark  lengths  contains  the  results  of  Voege,  Ann.  der  Phys.  14,  1904,  using  alternating  current 
id  "dull  point"  electrodes,  and  the  results  with  steady  potential  found  '    " 


and 

ler,  Ann.  d.  Phys.  29,  1909. 


in  the  recent  very  careful  work  of  C.  Miil- 


EJ 


22  cm. 


The  specially  constructed  elec- 
trodes for  the  columns  headed 
"  cup  electrodes  "  had  the  form  of 
a  projecting  knob  3  cm.  in  diame- 
ter and  having  a  height  of  4.5  mm. 
and  1.5  mm.  respectively,  attached 
to  the  plane  face  of  the  electrodes. 
These  electrodes  give  a  very  satis- 
linear relation  between  the 
lengths  and  the  voltage 
ut  the  range  studied. 


TABLE  258.  — Effect  of  the  Pressure  of  the  Gas  on  the  Dielectric  Strength. 
Voltages  are  given  for  different  spark  lengths  /. 


Pressure, 
cm.  Hg. 

7=0.04 

/=o.o6 

7=o.o8 

/=O.IO 

/=0.20 

l=o  30 

/=o.4o 

7=0.50 

2 

_ 

_ 

_ 

_ 

744 

939 

IIIO 

1266 

4 

- 

483 

567 

648 

1015 

1350 

1645 

1915 

6 

— 

S82 

690 

795 

1290 

1740 

2140 

2505 

10 

- 

771 

933 

1090 

1840 

2450 

3OI5 

358o 

15 

.. 

1060 

1280 

1490 

2460 

3300 

4080 

4850 

25 

IIIO 

1420 

1725 

2040 

3500 

4800 

6000 

7120 

35 

1375 

1820 

222O 

2615 

45°5 

6270 

7870 

9340 

45 

1640 

2150 

2660 

3120 

5475 

7650 

9620 

11420 

55 

1820 

2420 

3025 

3610 

6375 

8950 

11290 

13455 

65 
75 

2040 
2255 

2720 
3035 

3400 
3805 

4060 
4565 

7245 
8200 

1  0210 
II570 

12950 
14650 

15470 
1745° 

This  table  is  based  upon  the  results  of  Orgler,  1899.  See  this  paper  for  work  on  other  gases  (or  Landolt-Bornstein- 
Meyerhoffer). 

For  long  spark  lengths  in  various  gases  see  Voege,  Electrotechn.  Z.  28,  1907.  For  dielectric  strength  of  air  and  CO2 
in  cylindrical  air  condensers,  see  Wien,  Ann.  d.  Phys.  29,  1909. 

SMITHSONIAN  TABLES. 


250  TABLES  259,  260. 

DIELECTRIC  STRENGTH. 

TABLE  259.  — Dielectric  Strength  o!  Materials. 
Potential  necessary  for  puncture  expressed  in  kilovolts  per  centimetre  thickness  of  the  dielectric. 


Substance. 

Kilovolts 
per  cm. 

Substance. 

Kilovolts  1 
per  cm. 

Substance. 

Kilovolts 
per  cm. 

Ebonite    .... 

3OO~IIOO 

Oils  :                           Thickness. 

Papers  : 

Empire  cloth    .    . 

80-300 

Castor                 0.2  mm. 

190 

Beeswaxed  .    . 

770 

"       paper  .    . 
Fibre    

45° 
2O 

I.O      " 

Cottonseed  .... 

130 

7O 

Blotting  .    .    . 
Manilla 

ISO 

•7C 

Fuller  board      .     . 

200-300 

Lard                    0.2     " 

fv 

140 

Paraffined    !    ! 

Z5 

500 

Glass    

1OO-I  COO 

"                               I.O      " 

4.O 

Varnished 

100—2*50 

Granite  (fused) 

j  w    x  yw 

go 

Linseed,  raw      0.2    " 

mpj 

^5 

Paraffine  : 

Guttapercha  .     .     . 

80-200 

"              "            I.O      " 

9° 

Melted     .    .     . 

75 

Impregnated  jute  . 

20 

boiled  0.2    « 

190 

Melt  point. 

Leatheroid    .    .     . 

30-60 

"         I.O     " 

80 

Solid        43° 

35° 

Linen,  varnished  . 

I  OO—2OO 

CQ 

"            47° 

/too 

Liquid  air     ... 

40-90 

Neatsfoot           0.2    " 

Ow 
200 

T1/ 

"              52° 

T.WW 

230 

Mica  :          Thickness. 

"                           I.O      " 

9° 

a              7Qo 

450 

Madras  o.i  mm. 

I6OO 

Olive                  0.2    " 

170 

Presspaper  .    .    . 

45-75 

1.0      " 

300 

I.O      " 

75 

Rubber  .... 

160-500 

Bengal    o.i     " 

22OO 

Paraffin               0.2    " 

215 

Vaseline.    .    .    . 

90-130 

"           I.O      " 

700 

I.O     " 

160 

Thickness. 

Canada  o.i     " 

1500 

Sperm,  mineral  0.2    " 

1  80 

Xylol        0.2  mm. 

140 

I.O      " 

500 

I.O     " 

85 

1.0      " 

80 

South  America  . 

1500 

"       natural  0.2    " 

J95 

Micanite    .    .    . 

4000 

I.O      " 

90 

Turpentine         0.2    " 

160 

I.O     " 

no 

TABLE  260.— Potentials  In  Volts  to  Produce  a  Spark  In  Kerosene. 


Electrodes  Balls  of  Diam.  d. 

Spark  length. 

mm* 

0.5  cm. 

i  cm. 

a  cm. 

3  cm. 

0.1 

3800 

3400 

2750 

2200 

.2 

7500 

6450 

4800 

35°O 

•3 

10250 

945° 

745° 

4600 

•4 

11750 

10750 

9100 

5600 

.5 

13050 

12400 

IIOOO 

6000 

.6 

14000 

13550 

12250 

8250 

.8 

I.O 

15500 
16750 

15100 
16400 

13850 
15250 

10450 
12350 

Determinations  of  the  dielectric  strength  of  the  same  substance  by  different  observers  do  not  agree  well.  For  a  dis- 
cussion of  the  sources  of  error  see  Mo£cicki,  Electrotechn.  Z.  25,  1904. 

For  more  detailed  information  on  the  dependence  of  the  sparking  distance  in  oils  as  a  function  of  the  nature  of  the 
electrodes,  see  Edmondson,  Phys.  Review  6, 1898. 


SMITHSONIAN  TABLES. 


TABLE  261 . 


251 


ABSOLUTE   MEASUREMENTS  OF  CURRENT  AND  OF  THE   ELECTROMO- 
TIVE   FORCE   OF   STANDARD   CELLS. 


Date. 

Observer. 

Method. 

Electromotive 
Force  of 

Electrochemical 
Equivalent  found 
with  Voltameter  of 

Clark 
Cell 
at  ,5°. 

Weston 
Cell 
at  20°. 

Rayleigh 
Form. 

Porous 
Cup 
Form. 

volts. 

volts. 

mg. 

mg. 

1884 

F.  and  W.  Kohlrausch  4 

Tangent  galvanometer  . 
Filter  paper  voltameter 

1- 

1.1183 

1884 

Rayleigh  &  Sidgwick  .    < 

Current  balance  .    .     . 
Filter  paper  voltameter 

14345 

- 

I.II79 

1890 

Potier  and  Pellat    .    .    j 

Current  balance  .     .    . 
Filter  paper  voltameter 

- 

- 

I.II92 

1896 

Kahle    

Current  balance  . 

1.4.128 

1.0186 

I.Il82 

1898 

Patterson  and  Guthe  .    j 

Electrodynamometer    . 
Silver  oxide  voltameter 

I.II92 

1899 

Carhart  and  Guthe     .    . 

Electrodynamometer    . 

M333 

1903 

Pellat  and  Leduc    .    .    j 

Current  balance  .     .     . 
Leduc  voltameter     .    . 

1- 

- 

I.II95 

1904 

Van  Dijk  and  Kunst  .    j 

Tangent  galvanometer  . 
Filter  paper  voltameter 

- 

I.II82 

1906 

Guthe    

Electrodynamometer 

I.  A  77O 

i  0185 

I.II77 

1907 

Ayrton,  Mather  and  Smith 

Current  balance  .     .     . 

I4323 

1.01819 

1907 

Smith  and  Lowry     .     . 

Filter  paper  voltameter 

_ 

1.11827 

1908 

Janet,    Laporte    and      ( 

Filter  paper  voltameter 
Current  balance  ... 

1.0187 

I.II82 

1908 

Pellat     

Current  balance        .    . 

1.0184 

1908 

Guillet  

Current  balance  .    .     . 

- 

1.0182 

The  most  probable  value  of  the  Weston  cell  at  20°  is  1.0182  volts,  assuming  the  International 
ohm  to  be  io9  c.  g.  s.  units  and  the  volt  to  be  io8  c.  g.  s.  units.  The  corresponding  value  of  the 
Clark  cell,  as  prepared  at  present,  at  15°,  is  1.4324  volts. 

The  legal  values  of  the  Weston  cell,  however,  are  different  in  different  countries,  as  follows : 

United  States  (Bureau  of  Standards) 1.019125*  v.  at  20° 

Germany  (Physikalisch-Technische  Reichsanstalt) 1.0186  volts  at  20° 

England  (National  Physical  Laboratory) 1.0184  volts  at  20° 

The  value  of  the  Weston  standard  cell,  used  in  the  United  States,  is  based  upon  the  value 
adopted  by  the  Chicago  Electrical  Congress  (1893)  for  the  Clark  cell.  The  value  used  by  Ger- 
many was  adopted  in  1896,  and  is  based  on  Kahle's  work  at  the  Reichsanstalt.  The  value  used 
in  England  was  adopted  January  I,  1909,  and  is  based  on  the  recommendation  of  the  London 
Electrical  Conference  of  1908.  It  is  expected  that  a  new  value  will  soon  be  agreed  upon  by  the 
International  Committee  on  Electrical  Units  and  Standards,  which  will  be  adopted  generally  in  all 
countries. 

The  value  of  the  electrochemical  equivalent  of  silver  is  different  when  filter  paper  (Rayleigh 
form),  silk,  or  other  textile  is  used  to  separate  the  anode  from  the  cathode  from  what  it  is  when  a 
porous  cup  is  employed.  The  value  found  is  also  affected  by  the  addition  of  silver  oxide  to  the 
silver  nitrate  solution.  The  legal  value  in  all  countries  is  i.i  18  mg.  of  silver  per  coulomb,  and  this 
is  nearly  the  value  found  when  using  a  porous  cup  voltameter,  and  the  best  determinations  of  the 
current  that  have  been  made  by  absolute  current  balances.  Some  corrections  have  been  made  to 
the  figures  given  in  the  above  table  for  the  excess  due  to  filter  paper,  but  such  corrections  are  very 
uncertain. 

*  Based  on  1.0x89  at  25°  C. 
SMITHSONIAN  TABLES. 


252  TABLE  262. 

COMPOSITION  AND  ELECTROMOTIVE  FORCE  OF  VOLTAIC  CELLS. 

The  electromotive  forces  given  in  this  table  approximately  represent  what  may  be  expected  from  a  cell  in  good  work- 
ing order,  but  with  the  exception  of  the  standard  cells  all  of  them  are  subject  to  considerable  variation. 


(a)  DOUBLE  FLUID  CELLS. 

Name  of 
cell. 

Negative  pole. 

Solution. 

Positive 
pole. 

Solution. 

*£ 

asl 
w.s 

Bunsen  .    . 

Amalgamated  zinc 

(  I  part  H2SO4  to  ) 
(     12  parts  H2O  .  J 

Carbon 

Fuming  H2NO8 

1.94 

M 

«               « 

«« 

« 

HNO3,  density  1.38 

1.86 

Chromate  . 

«               « 

f  !2partsK2Cr2O7] 
to  25  parts  of  1 
|     H2SO4  and  100  f 
1    parts  H2O  .     .  J 

« 

(  i   part  H2SO4  to  ) 
I     12  parts  H2O    .  ( 

2.0O 

« 

«               « 

(  i  part  H2SO4  to  ) 
1     12  parts  H2O  .  J 

« 

C  12  parts  K2Cr2O7  ) 
I    to  100  parts  H2O  j 

2.03 

Daniell*   . 

«               «« 

(  i  part  H2SO4  to  ) 
}     4partsH20    .  J 

Copper 

(  Saturated  solution  ) 
I  of  CuSO4-f5H2O  f 

1.06 

« 

«               «< 

(  i  part  H2SO4  to  ) 
(      12  parts  H2O  .  J 

« 

« 

1.09 

« 

«               «« 

(  5%    solution    of  ) 
t    ZnS04  +  6H2CM 

« 

<« 

1.08 

« 

«               « 

(  i  part  NaCl   to  ) 
I     4  parts  H2O   .  ) 

ti 

« 

1.05 

Grove   .    . 

«               « 

(  i  part  H2SO4  to  ) 
(      12  parts  H2O  .  ) 

Platinum 

Fuming  HNOa  .    . 

i-93 

« 

««               « 

Solution  of  ZnSO4 

<« 

HNO3,  density  1.33 

1.66 

H 

«               « 

(  H2SO4  solution,  ) 
(      density  1.136  .  J 

«« 

Concentrated  HNO3 

i-93 

(1 

«               « 

(  H2SO4  solution,  ) 
(      density  1.136  .  J 

« 

HNO3,  density  1.33 

1.79 

« 

u               «« 

(  H2SO4  solution,  ) 
(      density  1.06    .  J 

« 

« 

1.71 

(( 

«               « 

(  H2SO4  solution,  ) 
(      density  1.14    .  ) 

« 

HNO3,  density  1.19 

1.66 

« 

«               <« 

(  H2SO4  solution,  ) 
\      density  1.06     .  ) 

K 

«           «            « 

1.61 

(( 

«               «< 

NaCl  solution  .    . 

«« 

"       density  1.33 

1.88 

Marie  Davy 

«               «< 

(  i  part  H2SO4  to  ) 
(      12  parts  H2O    ) 

Carbon 

(  Paste  of  protosul-  ) 
<    phate  of  mercury  > 
(    and  water  .     .     .  ) 

1.50 

Partz     .    . 

«               « 

Solution  of  MgSO4 

« 

Solution  of  K2Cr2O7 

2.06 

*  The  Minotto  or  Sawdust,  the  Meidinger,  the  Callaud,  and  the  Lockwood  cells  are  modifications  of  the  Daniell, 
and  hence  have  about  the  same  electromotive  force. 

SMITHSONIAN  TABLES. 


TABLE  262  (continued).  253 

COMPOSITION  AND  ELECTROMOTIVE  FORCE  OF  VOLTAIC  CELLS. 


Name  of  cell. 

Negative 
pole. 

Solution. 

Positive  pole. 

E.  M.  F. 
in  volts. 

(to)  SINGLE  FLUID  CELLS. 

Leclanche    .    .    . 

Amal.zinc 

(  Solution  of  sal-ammo-  ) 

Carbon.  Depolari- 
zer  :    manganese 
peroxide     with 

I46 

Chaperon    .    .    . 

«       tt 

(  Solution  of  caustic      1 

powdered  carbon 
j  Copper.  Depolar- 
j  izer  :  CuO  .    .    . 

0.98 

Edison-Lelande    . 
Chloride  of  silver 
Law                  .    . 

«        « 

Zinc    .    . 
« 

« 

23  %  solution  of  sal-  ) 
ammoniac  .    .     .    .  J 
IS  %          " 

<« 

(  Silver.    Depolari-  I 
(  zer  :  silver  chl'ride  j 
Carbon  •    •         . 

0.70 
1.02 
I.T7 

Dry  cell  (Gassner) 
Poggendorff     .    . 

H 

J.  Regnault  .    .    . 
Volta  couple 

«« 

Amal.zinc 
«i        «< 

«        « 
Zinc  .     . 

I  pt.  ZnO,  i  pt.  NH4C1,  "] 
3  pts.  plaster  of  paris, 
2  pts.  ZnCl2,and  water 
to  make  a  paste    .     . 
Solution   of  chromate 
of  potash    .    .    .     .  ( 
12  parts  K2Cr2O7  +    ) 
25  parts  H2SO4  -j-    > 
loo  parts  H2O    .    .  ) 
i  part  H2SO4  +           ) 
12  parts  H2O  +        >• 
i  part  CaSO4      .    .  ) 
H20 

u 

a 
u 

Cadmium    .    .    . 
CoDDer  . 

**J/ 

i-3 

1.08 

2.OI 

0-34 
O.Q8 

(0)  STANDARD  CELLS. 

Weston  normal    . 
Clark  standard    . 

jCadmi'm) 
{  am'lgamf 

j     Zinc     1 
am'lgamj 

(  Saturated  solution  of  ) 
t               CdS04              J 

(  Saturated  solution  of  \ 
\              ZnS04              1 

Mercury. 
Depolarizer:  paste 
of    Hg2SO4    and 
(CdS04    .     .     .    .4 
Mercury. 
Depolarizer:  paste 
1  of   Hg2SO4     and 
lZnS04    .    .    .     .. 

I.OIQI 

at  20°  C 

1-434* 
at  15°  C 

(d)  SECONDARY  CELLS. 

Lead  accumulator 

Lead  .    . 

(  H2SO4  solution  of        ) 

PbO2  

2  2f 

Reemier  (i^ 

CoDDer 

j      density  i.i       .     .     .  J 
CuSO4  +  H2SO4  .     . 

d 

(  1.68  to 
<  o  85,  av- 

"          (2).      .      . 

Main  

Amal.  zinc 
Amal.  zinc 

ZnSO4  solution  .     .    . 
H2SO4  density  ab't  i.i 

"    inH2SO4     . 
<i 

(  erage  1.3. 
2.36 
2.50 

Edison    .... 

Iron    .    . 

KOH  20  %  solution   . 

A  nickel  oxide    . 

(  i.i,  mean 
]    of  full 
(  discharge. 

-  *  E.  M.  F.  hitherto  used  at  Bureau  of  Standards.  See  p.  251.  The  temperature  formula  is  Et=  £20  —  0.0000406 
(t — 20)  —  0.00000095  (t— 2o)2  -}-  o.oooooooi  (t— 20)3.  The  value  given  is  that  adopted  by  the  Chicago  International 
Electrical  Congress  in  1893.  The  temperature  formula  is  Et  =  E1B  —  o.ooi  19  (t— 15)  —  0.000007  (*~  J5)*« 

t  F.  Streiutz  gives  the  following  value  of  the  temperature  variation  —  at  different  stages  of  charge  : 

dt 

E.  M.  F.  1.9223      1.9828      2.0031      2.0084      2.0105      2.0779      2.2070 

dE/dtXio«  140  228  335  285  255  130  73 

Dolezalek  gives  the  following  relation  between  E.  M.  F.  and  acid  concentration  : 
Per  cent  H,SO4  64.5  52.2  35.3  21.4  5.* 
E.M.F.,  o°C  2.37  2.25  2.10  2.00  1.89 

SMITHSONIAN  TABLES. 


254 


TABLE  263. 


CONTACT   DIFFERENCE   OF 

Solids  with  Liquids  and 
Temperature  of  substances 


c 

•s 

3 

1 

a 

3 

I 

d 
P 

N 

Distilled  water  

(.01 

<  to 

<      IU 

.269 
to 

.148 

171 

^.285) 

}     to   > 

<        to 

.1/1 

It 

*  7  / 

(•!7 

.100 

(  -345  ) 

(  *4~.i  ^6 

Alum  solution  :  saturated 
at  i6°-5  C  

—.127 

—653 

—•139 

.246 

—.225 

—536 

Copper  sulphate  solution  : 

sp.  gr.  1.087  at  i6°.6  C. 

•• 

.103 

— 

— 

— 

— 

— 

Copper  sulphate  solution  : 
saturated  at  I5°C.   .     . 

- 

.070 

- 

- 

- 

- 

- 

Sea  salt  solution:  sp.  gr. 
1.18  at  20°.5  C.     .     .     . 

- 

—475 

-.605 

- 

-.856 

—•334 

-.565 

Sal-ammoniac      solution  : 
saturated  at  150.5  c-     • 

- 

-396 

-.652 

~.I89 

•059 

-.364 

—  637 

Zinc  sulphate  solution  :  sp.  ) 

__0 

gr.  1.125  at  i6°9  C.  .    .    ) 

~ 

—.238 

Zinc    sulphate    solution  : 

saturated  at  I5°.3  C.     . 

— 

— 

~* 

— 

— 

— 

—430 

One  part  distilled  water  + 

3    parts    saturated    zinc 

_ 

_ 

_ 

_ 

_ 

_ 

—  444 

sulphate  solution  .     .     . 

Strong    sulphuric    acid    in 
distilled  water  : 

i  to  20  by  weight     .    .     . 

- 

. 

_ 

_ 

_ 

_ 

—•344 

i  to  10  by  volume    .    .    . 

(  about  \ 

I  —  .035  ) 

i  to  5  by  weight  .... 

- 

-  • 

- 

- 

- 

- 

(  .01 

5  to  i  by  weight  .... 

<  to 

- 

- 

—  .120 

- 

-•25 

- 

(  -55 

(   -72 

J«3   ) 

Concentrated  sulphuric  acid 

\  to 

1.113 

. 

)    to 

to    > 

_ 

« 

(-85 

(  1.252 

1.6   ) 

Concentrated  nitric  acid 

_ 

_ 

.672 

_ 

_ 

VTercurous  sulphate  paste  . 
Distilled  water  containing  ) 
trace  of  sulphuric  acid      ) 

- 

- 

- 

- 

- 

—.241 

*  Everett's  "  Units  and  Physical  Constants:  "  Table  of 


SMITHSONIAN  TABLES. 


TABLE  263 


255 


POTENTIAL    IN    VOLTS. 

Liquids  with  Liquids  In  Air.* 
during  experiment  about  16°  C. 


0 

| 

M 

c  . 

•so 

|| 

1 

& 

K 

Ij 

4)  ^ 

31 

i 

. 

•43  rt 

!« 

ii 

i- 

«  « 

•§.•8 

tio 

| 

. 

4 

5" 

jjj 

8« 

6? 

H 

s 

M 

'rt  o 

I 

1 

'•§ 

3 

It 

£~  2 

1* 

1+ 

tn 

.100 

.164 

Alum  solution  :  saturated 

•  A  V4J. 

at  16°  5  C    .             .    . 

— 

—.014 

— 

— 

~ 

— 

~ 

— 

"• 

*~ 

Copper  sulphate  solution  : 

sp.gr.  1.087  at  i6°.6  C. 
Copper  sulphate  solution  : 
saturated  at  15°  C.   .     . 

„ 

- 

_ 

—.043 

. 

- 

.090 

•095 

.102 

- 

Sea  salt  solution:  sp.  gr. 

1.18  at  20°-5  C.     .     .    . 

—  435 

Sal-ammoniac      solution  : 
saturated  at  15°.  5  C.     . 

- 

—348 

- 

- 

- 

- 

- 

- 

- 

- 

Zinc    sulphate    solution  :  ) 

sp.  gr.  1.125  at  l6°-9  C.    J 

Zinc    sulphate     solution  :  ) 
saturated  at  i5°.3  C.     .    J 

-.284 

- 

- 

—  .200 

- 

^.095 

- 

- 

- 

- 

One  part  distilled  water  -{-  ) 
3    parts    saturated   zinc  > 

_ 

_ 

_ 

_ 

_ 

—  .IO2 

_ 

_ 

_ 

_ 

sulphate  solution      .     .    ; 

Strong    sulphuric    acid    in 

distilled  water  : 

i  to  20  by  weight     .     .    . 

- 

- 

- 

- 

- 

- 

- 

- 

- 

- 

i  to  10  by  volume    .    .    . 

-.358 

- 

- 

- 

- 

- 

- 

- 

- 

- 

i  to  5  by  weight  .... 

.429 

- 

- 

- 

- 

- 

- 

- 

- 

- 

5  to  i  by  weight  .... 

- 

—  .016 

- 

- 

- 

- 

- 

- 

- 

- 

Concentrated  sulphuric  acid 

.848 

- 

- 

1.298 

1.456 

1.269 

- 

1.699 

- 

- 

Concentrated  nitric  acid 

_ 

_ 

__ 

_ 

_ 

_ 

_ 

_ 

Mercurous  sulphate  paste  . 

- 

- 

475 

- 

- 

- 

- 

- 

- 

- 

Distilled  water  containing  ) 
trace  of  sulphuric  acid  .    J 

— 

— 

— 

•* 

•* 

"• 

•• 

~ 

.078 

Ayrton  and  Perry's  results,  prepared  by  Ayrton. 
SMITHSONIAN  TABLES. 


2$6  TABLE  264. 

CONTACT  DIFFERENCE  OF  POTENTIAL  IN  VOLTS. 

Solids  with  Solids  in  Air.* 

The  following  results  are  the  "  Volta  differences  of  potential,"  as  measured  by  an  electrometer. 
They  represent  the  difference  of  the  potentials  of  the  air  near  each  of  two  metals  placed  in  con- 
tact. This  should  not  be  confused  with  the  junction  electromotive  force  at  the  junction  of  two 
metals  in  metallic  contact,  which  has  a  definite  value,  proportional  to  the  coefficient  of  Peltier 
effect.  The  Volta  difference  of  potential  has  been  found  to  vary  with  the  condition  of  the  me- 
tallic surfaces  and  with  the  nature  of  the  surrounding  gas.  No  great  reliance,  therefore,  can  be 
placed  on  the  tabulated  values. 

The  temperature  of  the  substances  during  the  experiment  was  about  18°  C. 


Carbon. 

Copper. 

Iron. 

Lead. 

Platinum. 

Tin. 

Zinc. 

Zinc 
amal- 
gam. 

Brass. 

Carbon  .     .    . 

0 

•370 

•485 

.858 

•"3 

•795 

i.096t 

I.2o8f 

.414! 

Copper  .    .    . 

—•370 

0 

.146 

•542 

-.238 

.456 

•750 

.894 

.087 

Iron  .... 

—  4»5t 

—.146 

0 

•401  1 

-.369 

•3'3t 

.6oot 

•744t 

-.064 

Lead      .    .    . 

—.858 

—•542 

—401 

0 

—.771 

—.099 

.210 

•357t 

—.472 

Platinum    .     . 

—  ii3t 

.238 

.369 

.771 

0 

.690 

.981 

I.I25t 

.287 

Tin    .... 

—  -795t 

—458 

—.313 

.099 

-.690 

o 

.281 

•463 

—•372 

Zinc  .... 

—  1.0961 

—.750 

—.600 

-.216 

-.081 

.281 

O 

.144 

—.679 

"    amalgam 

—  i.2o8f 

-.894 

—•744 

-357t 

-I.I25t 

—•463 

—.144 

o 

—.822 

Brass     .    .    . 

—.414 

-.087 

.064 

472 

-.287 

•372 

.679 

.822 

O 

The  numbers  not  marked  were  obtained  by  direct  experiment,  those  marked  with  a  dag- 
ger by  calculation,  on  the  assumption  that  in  a  compound  circuit  of  metals,  all  at  the  same 
temperature,  there  is  no  electromotive  force. 
The  numbers  in  the  same  vertical  column  are  the  differences  of  potential  in  volts  between 
the  substance  named  at  the  top  of  the  column  and  the  substance  named  on  the  same  line  in 
the  first  column,  when  the  two  substances  are  in  contact. 
The  metals  used  were  those  ordinarily  obtained  in  commerce. 

*  Everett's  "  Units  and  Physical  Constants."    The  table  is  from  Ayrton  and  Perry's  experiments,  and  was  pre- 
pared by  Ayrton. 

SMITHSONIAN  TABLES. 


TABLE  265. 


257 


DIFFERENCE    OF    POTENTIAL    BETWEEN    METALS    IN    SOLUTIONS    OF 

SALTS. 


The  following  numbers  are  given  by  G.  Magnanini  *  for  the  difference  of  potential  in  hundredth*  of  a  volt  between 
zinc  in  a  normal  solution  of  sulphuric  acid  and  the  metals  named  at  the  head  of  the  different  columns  when  placed 
in  the  solution  named  in  the  first  column.  The  solutions  were  contained  in  a  U-tube,  and  the  sign  of  the  differ- 
ence of  potential  is  such  that  the  current  will  flow  from  the  more  positive  to  the  less  positive  through  the  ex- 
ternal circuit. 


Strength  of  the  solution  in 
gramme  molecules  per 
fitre. 

Zinc.t 

Cadmium,  f 

Lead. 

Tin. 

Copper. 

Silver. 

No.  of 
molecules. 

Salt. 

Difference  of  potential  in  centivolts. 

0-5 
I.O 

H2S04 
NaOH 

0.0 
—32.1 

36.6 
19-5 

3!J 

51-3 
0.2 

100-7 
80.2 

121.3 

95-8 

I.O 

KOH 

—42.5 

15.5 

32.0 

—  1.2 

77-0 

104.0 

I.O 

Na2S04 
Na2S2O8 

1.4 

—5-9 

35-6 
24.1 

50.8 
45-3 

51-4 

457 

101.3 
38.8 

120.9 
64.8 

I.O 
I.O 

KN08 
NaNOa 

ii.Sj 
"•5 

32-3 

42.6 
51.0 

40.9 

8l.2 

957 

105.7 
114.8 

0.5 

K2CrO4 

23-9* 

42.8 

41.2 

40.9 

94.6 

I2I.O 

°-5 

K2Cr207 

72.8 

61.1 

78.4 

68.1 

123.6 

132.4 

0.5 

K2S04 

1.8 

347 

51-0 

40.9 

957 

II4.8 

o-5 
0.25 
0.167 

(NH4)2S04 
K4FeC6N6 
K6Fe2(CN)2 

—6.1 

4I.O§ 

37-1 
33-6 
80.8 

53-2 
£2 

57-6J 
41.2 
130.9 

101.5 
110.7 

1257 
87.8 
124.9 

I.O 

KCNS 

—  1.2 

32-5 

52.8 

527 

52-5 

72.5 

I.O 

NaNOa 

4-5 

35-2 

50.2 

49.0 

103.6 

104.6? 

0.5 

SrNOa 

14.8 

38.3 

50.6 

48.7 

103.0 

"9-3 

0.125 

I.O 

Ba(N08)2 
KNO8 

21.9 

39-3 
35-6 

47-5 

52.8 
49-9 

109.6 
104.8 

121.5 
115.0 

0.2 

KC1O« 

15-IOj 

39-9 

53-8 

577 

'05-3 

1  20.0 

0.167 

KBrOa 

13-20* 

40.7 

50.9 

111.3 

120.8 

I.O 
I.O 

NH4C1 
KF 

11 

324 
22.5 

41.1 

50-9 
50.8 

81.2 
61.3 

IOI.7 
61.5 

I.O 

NaCl 

— 

3*-9 

51.2 

50.3 

80.9 

IOI-3 

I.O 

KBr 

2-3 

47.2 

73-6 

82.4 

I.O 

KC1 

32.1 

51.6 

52^6 

81.6 

107.6 

0.5 

NagSOa 

—8.2 

28.7 

41.0 

31.0 

68.7 

1037 

-II 

NaOBr 

18.4 

41.6 

73-  I 

70.6  J 

89.9 

997 

I.O 

C4H606 

5-5 

397 

61.3 

54-4§ 

104.6 

123.4 

o-S 

C4H606 

4.1 

41-3 

61.6 

57.6 

110.9 

1257 

0.5 

C4H4KNaO6 

—7.9 

5i-5 

42-47 

100.8 

119.7 

SMITHSONIAN  TABLES. 


*  "  Rend,  della  R.  Ace.  di  Roma,"  1890. 

t  Amalgamated. 

$  Not  constant. 

§  After  some  time. 

II  A  quantity  of  bromine  was  used  corresponding  to  NaOH  =  x. 


258 


TABLE  266. 
THERMOELECTRIC  POWER. 


The  thermoelectric  power  of  a  circuit  of  two  metals  is  the  electromotive  force  produced  by  one 
degree  C.  difference  of  temperature  between  the  junctions.  The  thermoelectric  power  varies  with 
the  temperature,  thus  :  thermoelectric  power  =  Q  =  dE  /dt  =  A  +  Bt,  where  A  is  the  thermoelec- 
tric power  at  o°  C.t  B  is  a  constant,  and  /  is  the  mean  temperature  of  the  junctions.  The  neutral 
point  is  the  temperature  at  which  dE  /dt  =  o,  and  its  value  is  —  A  /B.  When  a  current  is  caused 
to  flow  in  a  circuit  of  two  metals  originally  at  a  uniform  temperature,  heat  is  liberated  at  one  of 
the  junctions  and  absorbed  at  the  other.  The  rate  of  production  or  liberation  of  heat  at  each 
junction,  or  Peltier  effect,  is  given  in  calories  per  second,  by  multiplying  the  current  by  the  co- 
efficient of  the  Peltier  effect.  This  coefficient  in  calories  per  coulomb  =  Q  T/J,  in  which  Q  is  in 
volts,  T is  the  absolute  temperature  of  the  junction,  and  7=4.19.  Heat  is  also  liberated  or  ab- 
sorbed in  each  of  the  metals  as  the  current  flows  through  portions  of  varying  temperature.  The 
rate  of  production  or  liberation  of  heat  in  each  metal,  or  the  Thomson  effect,  is  given  in  calories 
per  second  by  multiplying  the  current  by  the  coefficient  of  the  Thomson  effect.  This  coefficient, 
in  calories  per  coulomb,  =  BTQ /y,  in  which  B  is  in  volts  per  degree  C.,  T  is  the  mean  absolute 
temperature  of  the  junctions,  and  0  is  the  difference  of  temperature  of  the  junctions.  (BT)  is  Sir 
W.  Thomson's  "  Specific  Heat  of  electricity."  The  algebraic  signs  are  so  chosen  in  the  following 
table  that  when  A  is  positive,  the  current  flows  in  the  metal  considered  from  the  cold  junction  to 
the  hot.  When  B  is  positive,  Q  increases  (algebraically)  with  the  temperature.  The  values  of 
A,  By  and  thermoelectric  power,  in  the  following  table  are  with  respect  to  lead  as  the  other  metal 
of  the  thermoelectric  circuit.  The  thermoelectric  power  of  a  couple  composed  of  two  metals,  I 
and  2,  is  given  by  subtracting  the  value  for  2  from  that  for  i  ;  when  this  difference  is  positive,  the 
current  flows  from  the  cold  junction  to  the  hot  in  I.  In  the  following  table,  A  is  given  in  micro- 
volts, B  in  microvolts  per  degree  C.,  and  the  neutral  point  in  degrees  C. 

The  table  has  been  compiled  from  the  results  of  Becquerel,  Matthiessen  and  Tait ;  in  reducing 
the  results,  the  electromotive  force  of  the  Grove  and  Daniell  cells  has  been  taken  as  1.95  and 
1.07  volts.  The  value  for  constantin  was  reduced  from  results  given  in  Landolt-Bornstein's 
tables.  The  thermoelectric  powers  of  antimony  and  bismuth  alloys  are  given  by  Becquerel  in  the 
reference  given  below. 


Substance. 

A 
Microvolts. 

B 

Microvolts. 

Thermoelectric  power 
at  mean  temp,  of 
junctions  (microvolts). 

Neutral 
point 
A. 
B 

Author- 
ity. 

20°  C. 

50°  C. 

0.76 
11.94 

-2.63 

—1-34 

—2.80 
—I7-I5 

—  2.22 

21.8 
83.57 

3-°4 

—0.0039 
0.0506 

—  0.0424 
—0.0094 
—  -O.OIOI 

0.0482 

0.0000- 

0.0094 
0.0506  / 

—0.2384 
0.0506 

0.68 
—6.0 
—22.6 
—  26.4 
—17.0 
12.95 

I3-56 
97.0 
89.0 
65.0 

45-0 
-3-48 

22. 

""       if 
—1-52 
—  O.IO 

-3-8 

—  1.2 

-3.o 
—  16.2 

—17-5 

0.00 

—2.03 
0.413 

22.8 

0.56 

1447 
12.7 

39-9 

—4-75 
—2.45 

+19-3 
—  i  .81 

—3-30 
—14.74 

—  12.10 
—  9.IO 
0.00 

—1-75 

3-30 
15-50 
24-33 

195 
—236 

—62 

—143 

[-277] 
356 

236 
[-431] 

T 

M 

« 

« 

B 
T 
B 

M 
« 

« 
« 
« 
B 
T 
B 
M 

T 

M 

n 

H 

T 

« 

M 

B 

« 

T 

M 

B 

« 

T 
« 

« 

Antimony,  comm'l  pressed  wire 
"           axial  

equatorial   .... 
"           ordinary      .... 
Argentan                   .    .         . 

«i 

Arsenic  

Bismuth,  comm'l  pressed  wire  . 
"         pure            "         "     . 
"         crystal,  axial  .... 
"        equatorial  .     . 
"         commercial  .... 

Cobalt    

CoDDer   . 

commercial      .... 
"       galvanoplastic  .... 
Gold  

M 

"    pianoforte  wire     .... 
"    commercial  ...... 

«            « 

Lead  

«< 

Nickel    

«      (_  i8°toi75°)  .    .    .    . 

"         (2SOO-3000)     

"      (above  340°)  

SMITHSONIAN  TABLES* 


TABLES  266 
THERMOELECTRIC  POWER. 

TABLE  266.  —  Thermoelectric  Power  (continued). 


259 


Substance. 

A 
Microvolts. 

B 

Microvolts. 

Thermoelectric  power 
at  mean  temp,  of 
junctions  (microvolts). 

Neutral 
point 
A 

Author- 
ity. 

20°  C. 

50°  C. 

B' 

Palladium  

6.18 

-257 
0.60 

—7.90 
-5.90 
-6.15 

—2.12 
—11.27 

0-43 
—2.32 

0.0355 

0.0074 
O.OIO9 

—  0.0062 
0.0133 

—0.0055 

—  0.0147 
0.0325 

—  o.oo5«5 
—  0.0238 

6.9 

—29.9 
—0.9 
—2.42 
8.82 

—8.03 

m 

—807. 
—2.41 
—  3-OO 

—  10.62 
—502. 

—  O.I 

0,33 
—2.79 
—3-7    , 

7-96 
6.9 

—  2.20 

«-*s 

—0.94 
2.14 

—8.21 

-5-23 
—  6.42 

—2.86 

—  2.18 
—9-65 

—429-3 
—0.33 

0,1  6 
—3-51 

—174 

347 

-55 

[—1274] 

444 

[4118] 
—144 

,347 

7"8o 

-98 

T 
B 

M 

T 

« 

B 

« 

T 

« 
« 

M 
T 
M 
B 
T 
M 
B 

M 
T 

M 

« 

Phosphorus  (red)    

"          (hardened)    .... 
(malleable)   .... 
"         wire     

another  specimen  .     . 
Platinum-iridium  alloys  : 
85%Pt+i5%Ir   .... 
9o%Pt+io%Ir    .... 
95%Pt+5%Ir   .... 

"      (pure  hard)    

Steel      

« 

u 

« 

Zinc  

TABLE  267.— Thermoelectric  Power  against  Platinum. 

One  junction  is  supposed  to  be  at  o°  C ;  +  indicates  that  the  current  flows  from  the  o°  junction 
into  the  platinum.     The  rhodium  and  indium  were  rolled,  the  other  metals  drawn.* 


Tempera- 
ture, °  C. 

Au. 

Ag. 

io%Pd. 

IO%Pt+ 

oo%Pd. 

Pd. 

00%Pt+ 

io%Rh. 

oo%Pt+ 
io%Ru. 

Ir. 

Rh. 

-I85 

—0.15 

—  0.16 

—O.I  I 

+0.24 

+0.77 

— 

—0-53 

—0.28 

—0.24 

—80 
+  IOO 

70.31 

+0.74 

—  0.30 
+0.72 

—0.09 
+0.26 

+0.15 
—0.19 

+0-39 
—  0.56 

__ 

—  °-39 
+0.73 

—0.32 
+0.65 

—0.31 
+0.65 

+  200 

+1.8 

+1-7 

+0.62 

—0.31 

—  1.20 

— 

+1.6 

-I.e 

+  I.C 

+300 

+3-0 

+3-o 

+  1.0 

—0-37 

—  2.0 

+2-3 

+2.6 

+2.5 

+  2.6 

+400 

+4-5 

+4-5 

+1.5 

—0.35 

—2.8 

+3-2 

+3-6 

-3-6 

+37 

+5°° 

+600 
+700 

+6.1 
+7-9 
+9-9 

+6.2 
+8.2 

+10.6 

+1.9 

+2.4 

+2.9 

-o.i  8 

-O.I  2 

-0.61 

-3-8 
-4.9 

—6-3 

+4-1 
+5-1 

+6.2 

-5-7 
^6.9 

: 

-4.8 
-6.1 

S 

+8.? 

+800 

+  12.0 

+13.2 

-1.2 

—7-9 

+7.2 

- 

-8.0 

-9.1 

+9-9 

+900 

+  H.3 

+16.0 

+3.8 

-2.1 

-9.6 

+8.3 

-9.2 

+  10.8 

+  H7 

+  1000 
+  IIOO 

+(1300) 
+(1500) 

+  16.8 

~      X 

- 

+4.3 

+4.8 

-4.2 

—"•5 
—13-5 

+9.5 

+  10.6 

tI3i 

+15-6 

+10.4 
+  11.6 
+  '4.2 
+16.9 

+  12.6 

+  14-5 
+  18.6 

+23-1 

fer? 

+20.4 
+25.6 

SMITHSONIAN  TABLES. 


*  Holborn  and  Day. 


26o 


TABLE  268. 
PELTIER  EFFECT, 


The  coefficient  of  Peltier  effect  may  be  calculated  from  the  con- 
stants A  and  B  of  Table  255,  as  there  shown.  Experimental  re- 
sults, expressed  in  slightly  different  units,  are  here  given.  The 
figures  are  for  the  heat  production  at  a  junction  of  copper  and  the 
metal  named,  in  calories  per  ampere-hour.  The  current  flowing 
from  copper  to  the  metal  named,  a  positive  sign  indicates  a  warm- 
ing of  the  junction.  The  temperature  not  being  stated  by  either 
author,  and  Le  Roux  not  giving  the  algebraic  signs,  these  results 
are  not  of  great  value. 


Metals. 

Calories  per  ampere-hour. 

Jahn.* 

Le  Rouz.f 

Antimony  (Becquerel's)} 

- 

13.02 

"           (commercial) 

- 

4.8 

Bismuth  (pure) 

- 

19.1 

"        (Becquerel's)§ 

- 

25.8 

Cadmium         .        .        • 

—  0.616 

0.46 

German  silver  .        .        . 

- 

2.47 

Iron         •        •        •       • 

—3-613 

2-5 

Nickel     .... 

4.362 

Platinum  .... 

0.320 

Silver       .... 

—0.413 

Zinc         .... 

-0.585 

o-39 

«  "  Wied.  Ann."  vol.  34,  p.  767. 

t  "  Ann.  de  Chim.  et  de  Phys."  (4)  vol.  10,  p,  aoi. 

j  Becquerel's  antimony  is  806  parts  Sb+4o6  parts  Zn+zai  parts  Bi. 

§  Becquerel's  bismuth  is  10  parts  Bi-f- 1  part  Sb. 

SMITHSONIAN  TABLES. 


TABLE  269. 
VARIOUS  DETERMINATIONS  OF  THE  VALUE  OF  THE  OHM. 


26l 


Date. 

Observer, 

Method. 

Value  of 
B.  A.  unit  in 
ohms. 

Value  of  Sie- 
mens unit, 
B.  A.  unit. 

Value  of 
ohm  in  cms. 
of  Hg. 

1882 
1883 

Lord  Rayleigh         . 
Lord  Rayleigh 

Rotating  coil 
Lorenz  method 

0.98651 
.98677 

0.95412 
.95412 

106.24 

106.21 

1884 
1887 

Mascart   . 
Rowland  .        . 

Induced  current 
Mean  of  several  methods 

.98611 
.98644 

•95374 
.95349 

106.33 
106.32 

1887 

Kohlrausch 

Damping  of  magnets 

.98660 

.95338 

106.32 

1882) 
1888) 

Glazebrook      . 

Induced  currents    . 

.98665 

.95352 

106.29 

1     1890 

Wuilleumeier  . 

Mean  effect  of  induced 

1890 
1891 

Duncan  and  Wilkes 
Jones 

currents 
Lorenz  method 
Lorenz  method 

.98686 
.98634 

•95355 
•95341 

106.31 
106.34 
106.31 

1894 

Jones 

Lorenz  method 

— 

_ 

io6.*n 

1895 

Himstedt 

Mean  effect  of  induced 

«JJ 

current 

_ 

M 

106.28 

1897 
1899 

Ayrton  and  Jones    . 
Guillet     . 

Lorenz  method 
Mean  effect  of  induced  cur 
a  calibrated  icoo-ohm  c 

(.98634) 
rent,  using 
ail    ... 

_ 

106.27 
106.20 

Means 

0.98651 

0.95366 

106.288 

1883 

1884 

Wild 
Wiedemann 

Damping  of  magnet 
Earth  inductor 

- 

- 

106.03 
106.19 

1884 

H.  F.  Weber  . 

Induced  current 

_ 

_ 

K>5.37 

1884 

H.  F.  Weber  . 

Rotating  coil  . 

_ 

— 

J  +J* 

IOO.IO 

1884 
1885 

Roiti 
Himstedt 

Mean  effect  of  induced  current,  using 
German  silver  coils  certified  by  makers 
Mean  effect  of  induced  current,  using 

- 

105.89 

1885 
1889 

Lorenz     .        .        . 
Dorn 

Gennan  silver  coils  certifie 
Lorenz  method 
Damping  of  magnet 

d  by  makers 

- 

105.98 
105.93 

106.24 

The  legal  value  of  the  ohm  is  the  resistance  of  a  column  of  mercury  of  uniform  cross-section, 
weighing  14.4521  gms.,  and  having  a  length  of  106.30  cms.  This  is  known  as  the  international 
ohm.  Mercury  ohms  conforming  to  these  specifications  have  been  prepared  in  recent  years  at 
the  Physikalisch-Technische  Reichsanstalt  and  the  National  Physical  Laboratory,  and  are  now 
being  set  up  at  the  Bureau  of  Standards.  The  wire  standards  of  resistance  at  the  above-named 
laboratories  agree  in  value  to  within  two  parts  in  looooo.  Hence  there  is  a  very  close  agreement 
in  the  values  of  precision  resistances  calibrated  at  these  laboratories. 

SMITHSONIAN  TABLES. 


262 


TABLE  270. 


SPECIFIC  RESISTANCE  OF  METALLIC  WIRES, 


This  table  is  modified  from  the  table  compiled  by  Jenkin  (1862)  from  Mattoiessen's  results  by  taking  the  resistance  of 
silver,  gold,  and  copper  from  the  observed  metre  gramme  value  and  assuming  the  densities  found  by  Matthiessen, 
namely,  10.468,  19.265,  and  8.95. 


Substance. 

*o  o 
CJ  bo  . 

1 

Resistance  at  o°  C.  of  a 
wire  one  metre  long, 
one  mm.  in  diam. 

Resistance  at  o°  C.  of  a 
wire  one  metre  long, 
weighing  one  gramme. 

Resistance  at  o°  C.  of  a  1 
wire  one  foot  long, 
icW  in-  in  diam. 

Resistance  at  o°  C.  of  a  1 
wire  one  foot  long, 
weighing  one  grain. 

Percentage  increase  of 
resistance  for  i°  C.  in- 
crease of  temp,  at  20°  C.  1 

Silver  annealed  . 

1.460  X  10-6 

0.01859 

.1523 

8.781 

.2184 

0-377 

"      hard  drawn 

1.585      « 

0.02019 

.1659 

9-538 

.2379 

- 

Copper  annealed        .        . 

1.584      " 

0.02017 

.1421 

9.529 

.2037 

0.388 

"     hard  drawn    .        . 

I.6I9      " 

O.O2062 

.1449 

9.741 

.2078 

- 

Gold  annealed    . 

2.088       « 

0.02659 

.4025 

12.56 

.5771 

0.365 

"    hard  drawn        .        . 

2.125      " 

0.02706 

.4094 

12.78 

.5870 

- 

Aluminium  annealed  . 

2.906      " 

0.03699 

.0747 

17.48 

.1071 

- 

Zinc  pressed       .        ... 

5.613       « 

0.07146 

.4012 

33-76 

'5753 

0.365 

Platinum  annealed 

9-035       " 

O.II50 

1-934 

54-35 

2.772 

- 

Iron               " 

9.693       « 

0.1234 

•7551 

58.31 

1.083 

- 

Nickel            « 

12.43       " 

0.1583 

L057 

74.78 

I.5I5 

- 

Tin  pressed 

13-18      " 

0.1678 

.9608 

79.29 

1-377 

0.365 

Lead     «             ... 

19.14      « 

0.2437 

2.227 

115.1 

3-193 

0.387 

Antimony  pressed 

3542      « 

0.4510 

2.379 

213.1 

3.410 

0.389 

Bismuth         " 

130.9        « 

1.667 

12.86 

787.5 

18.43 

0-354 

Mercury         " 

94.07       " 

1.198 

12.79 

565.9 

18.34 

0.072 

Platinum-silver,  2  parts  Ag,  ) 
i  part  Pt,  by  weight        .  ) 

24.33      " 

0.3098 

2.919 

146.4- 

4.186 

0.031 

German  silver     . 

20.89      " 

0.2660 

1.825 

I257 

2.617 

0.044 

Gold-silver,  2  parts  Au,     ) 

{ 

i  part  Ag,  by  weight      .  ) 

10.84      " 

0.1380 

1.646 

65.21 

2-359 

0.065 

SMITHSONIAN  TABLES. 


TABLE  271.  263 

SPECIFIC  RESISTANCE  OF  METALS. 

The  specific  resistance  is  here  given  as  the  resistance,  in  microhms,  per  centimetre  of  a  bar  one 
square  centimetre  in  cross  section. 


Substance. 

Physical  state. 

Specific  resistance. 

Temp.  °  C. 

Authority. 

Aluminum  .    . 

_ 

2.6-3.0 

0 

Various. 

Antimony  .     . 

Solid 

35-4-45-8 
182.8 

0 
Melting-point 

M 

De  la  Rive. 

"... 

Liquid 

129.2 

" 

M 

« 

— 

1377 

860 

" 

Arsenic  .    .    . 

- 

33-3 

0 

Matthiessen  and 

Vogt. 

Bismuth     .    . 

Electrolytic  soft 

108.0 

0 

Van  Aubel. 

"       ... 

hard 

108.7 

0 

" 

" 

Commercial 

110-268 

o 

Various. 

Boron     .    .    . 

Pulverized  and  com- 

( 

pressed 

8  X  id0 

_ 

Moissan. 

Cadmium   .    . 

_ 

6.2-7.0 

_ 

Various. 

M 

Solid 

16.5 

318 

Vassura. 

"... 

Liquid 

37-9 

318 

" 

Gold  .... 

— 

2.04-2.09 

o 

Various. 

Calcium      .    . 

_ 

7-5 

16.8 

Matthiessen. 

Cobalt    .    .    . 

_ 

9.8 

0 

Copper  .    .    . 

Annealed 

0 

Various. 

"  .     .    . 

Hard-drawn 

1.61-1.68 

0 

A 

Iron  .... 

Commercial 

9.7-12.0 

o 

« 

"     .    .    .    . 

Electrolytic 

It.) 

Ordinary 

Kohlrausch. 

M 

M 

105.5 

Red  heat 

• 

"      .      .      .      . 

«« 

114.8 

Yellow  heat 

« 

"      .      .      .      . 

« 

118.3 

Iron  magnetic 

heat 

« 

Steel.    .    .    . 

Cast 

19.1 

Ord.  temp. 

« 

*'..... 

«« 

85.8 

Red  heat 

« 

"    .    .    .    . 

• 

104.4 

Yellow  heat 

« 

"    .    .    .    . 

" 

"3-9 

Nearly  white 

heat 

.      « 

"    .    .    .    . 

Tempered  glass  hard 

457  (l  4-  .00161*) 

Barus  and 

Strouhal. 

«  :  :  :  : 

"        light  yellow 
"                yellow 

28.9  (i  4-  .00244*) 
26.3  (i  -j-  .00280*) 

J 

**.... 

blue 

20.5  (i  4-  -00330*) 

/ 

" 

**  .  .  .  . 

"        light  blue 

18.4  (i  4  .00360*) 

t 

« 

Iron  .... 

"        soft 
Cast,  hard 

15.9  (i  +  .00423*) 
97.8 

t 

0 

« 

"     .    .    .    . 

"     soft 

74-4 

0 

« 

Indium  .    .    . 

_ 

8.38 

.  o 

Erhard. 

Lead.    .    .    . 

«. 

18.4-19.6 

o 

Various. 

Lithium  .    .    . 

_ 

8.8 

20 

Matthiessen. 

Magnesium     . 

- 

4.1-5.0 

O 

Various. 

Nickel    .     .    . 

;        — 

10.7-12.4 

O 

" 

Palladium  .    . 

- 

10.6-13.6 

0 

a 

Platinum     .    . 

— 

9.0—15.5 

0 

ft 

Potassium  .    . 

_ 

25.1 

0 

Matthiessen. 

M 

Fluid 

504 

100 

M 

Silver     .    .    . 

,. 

o 

Various. 

Strontium  .     . 

• 

25-I3 

20 

Matthiessen. 

Tellurium  .    . 

_ 

2.17  X  lo6 

19.6 

« 

"... 

- 

55-05 

294 

Vincentini  and 

Omodei. 

Tin        ... 

. 

9-53-"-4 

o 

Various. 

... 

•, 

9-53 

0 

Vassura. 

... 

Solid 

-^   **v^ 

20.96 

226.5 

« 

.    .    . 

Liquid 

44.56 

226.5 

a 

Znc       ... 

— 

5.56-6.04 

o 

.    .    . 

Solid 

18.16 

Melting-point 

De  la  Rive. 

... 

Liquid 

36.00 

8 

SMITHSONIAN  TABLES. 


264 


TABLE  272. 


RESISTANCE   OF   METALS   AND 

The  electrical  resistance  of  some  pure  metals  and  of  some  alloys  have  been  determined  by  Dewar  and  Fleming  and 
increases  as  the  temperature  is  lowered.  The  resistance  seems  to  approach  zero  for  the  pure  metals,  but  not  for 
temperature  tried.  The  following  table  gives  the  results  of  Dewar  and  Fleming.* 

When  the  temperature  is  raised  above  o°  C.  the  coefficient  decreases  for  the  pure  metals,  as  is  shown  by  the  experi- 
experiments  to  be  approximately  true,  namely,  that  the  resistance  of  any  pure  metal  is  proportional  to  its  absolute 
is  greater  the  lower  the  temperature,  because  the  total  resistance  is  smaller.  This  rule,  however,  does  not  even 
zero  Centigrade,  as  is  shown  in  the  tables  of  resistance  of  alloys.  (Cf.  Table  262.) 


Temperature  =r 

100° 

20° 

0° 

—  80° 

Metal  or  alloy. 

Specific  resistance  in  c.  g.  s.  units. 

Aluminium,  pure  hard-drawn  wire  . 

4745 

3505 

3l6l 

- 

Copper,  pure  electrolytic  and  annealed  . 

1920 
2665 
I397ot 

19300 

1457 
208l 

9521 
13494 

1349 
1948 
86l3 

12266 

1400 
7470 

Nickel,  pure  (prepared  by  Mond's  process  ) 
from  compound  of  nickel  and  carbon  >  . 
monoxide)                                                    ) 

Platinum,  annealed          

10907 
2139 
13867 

8752 
1647 

10473 

8221 
1559 

9575 

6i33  " 
1138 
6681 

Tin,  pure  wire          

German  silver,  commercial  wire 

35720 

34707 

34524 

33664 

Palladium-silver,  20  Pd  +  80  Ag     . 

15410 

14984 

14961 

14482 

Phosphor-bronze,  commercial  wire 

9071 

8588 

8479 

8054 

Platinoid,  Martino's  platinoid  with  I  to  2%  ) 
tungsten                                                      J  ' 

44590 

43823 

43601 

43022 

Platmum-iridium,  80  Pt  +  20  Ir 

31848 

29902 

29374 

27504 

Platinum-rhodium,  90  Pt-f-  10  Rh  . 

18417 

14586 

13755 

10778 

Platinum-silver,  66.7  Ag  +  33.3  Pt  . 

27404 

26915 

26818 

26311 

Carbon,  from  Edison-Swan  incandescent) 
lamp                                                           J  * 

- 

4046XI08 

4092X108 

4189X108 

Carbon,  from  Edison-Swan  incandescent  ) 
lamp                                                            J  * 

3834X108 

3908XI08 

3955Xio8 

4054X108 

Carbon,  adamantine,  from  Woodhouse  and  ) 
Rawson  incandescent  lamp                       J  * 

6i68Xio« 

6300XIO« 

6363X10* 

6495X108 

*  "  Phil.  Mag."  vol.  34,  1892. 

t  This  is  given  by  Dewar  and  Fleming  as  13777  for  96°.4,  which  appears  from  the  other  measurements  too  high. 
SMITHSONIAN  TABLES. 


TABLE   272  (continued). 

ALLOYS  AT   LOW   TEMPERATURES. 


265 


by  Cailletet  and  Bouty  at  very  low  temperatures.  The  results  show  that  the  coefficient  of  change  with  temperature 
the  alloys.  The  resistance  of  carbon  was  found  by  Dewar  and  Fleming  to  increase  continuously  to  the  lowest 

ments  or  Miiller,  Benoit,  and  others.  Probably  the  simplest  rule  is  that  suggested  by  Clausius,  and  shown  by  these 
temperature.  This  gives  the  actual  change  of  resistance  per  degree,  a  constant ;  and  hence  the  percentage  of  change 
approximately  hold  for  alloys,  some  of  which  have  a  negative  temperature  coefficient  at  temperatures  not  far  from 


Temperature  = 

—  100° 

—  182° 

-197° 

Mean  value  of 
temperature  co- 

Metal or  alloy. 

Specific  resis 

tance  in  c.  g. 

s.  units. 

efficient  between 
—  100°  and 

+  100°  C.* 

Aluminum,  pure  hard-drawn  wire   . 

1928 

894 

- 

.00446 

Copper,  pure  electrolytic  and  annealed  . 
Gold  soft  wire         

757 

I2O7 

272 

604 

I78 

431 
•17  e 

4OIO 

1067 

608 

O/  J 

t78 

Nickel,  pure  (prepared  by  Mond's  process  ) 
from  compound  of  nickel  and  carbon  >  . 
monoxide)                                                    ) 

6110 

C2QC 

1900 
2821 

22QO 

538 

74.1 

Q62 

472 

777 

c6?i 

2CC-7 

428 

German  silver,  commercial  wire 

33280 

32512 

_ 

035 

Palladium-silver,  20  Pd  +  80  Ag    . 

14256 

13797 

- 

039 

Phosphor-bronze,  commercial  wire  . 

7883 

7371 

- 

070 

Platinoid,  Martino's  platinoid  with  I  to  2%  ) 
tungsten                                                       J 

42385 

4M54 

025 

Platinum-iridium,  80  Pt  +  20  Ir 

26712 

24440 

- 

087 

Platinum-rhodium,  90  Pt  +  10  Rh  . 

9834 

7134 

- 

3" 

Platinum-silver,  66.7  Ag  +  33.3  Pt  . 

26108 

25537 

- 

024 

Carbon,  from  Edison-Swan  incandescent  ) 
lamp                                                           ) 

42i8Xio» 

432IXI08 

- 

- 

Carbon,  from  Edison-Swan  incandescent  ) 
lamp                                                           J  ' 

4079X108 

4i8oXio8 

- 

031 

Carbon,  adamantine,  from  Woodhouse  and  \ 
Rawson  incandescent  lamp                        )  * 

6533X108 

- 

- 

O29 

*  This  is  a  in  the  equation  R=.R0(\-\-  a/),  as  calculated  from  the  equation  a 
SMITHSONIAN  TABLES. 


-^100  —  It— -io» 

200  Ka 


266  TABLE  273. 

CONDUCTIVITY  OF  THREE-METAL  AND  MISCELLANEOUS  ALLOYS. 

Conductivity  In  mhos  or —("*—£• 

ohms  per  cm.  cube 


E     Metals  and  alloys. 

Composition  by  weight. 

10* 

aXio« 

£ 

3 

Id-copper-silver  .    .    . 
i        «           « 

1               ««                      « 

58.3  Au  +  26.5  Cu  -f  15.2  Ag 
66.5  Au  -j-  15-4  Cu  -j-  18.1  Ag 
7.4  Au  +  78.3  Cu  +  14.3  Ag 

6*83 
28.06 

574 
529 
1830 

924 

7280 

I 

I 

1  iiickel-copper-zinc  .    .    . 

(  12.84  Ni  +  30.59  Cu  +       ) 
\  6.57  Zn  by  volume    .    .    .  f 

4.92 

444 

51 

I 

Brass      

Various 

1  2  2—1  C  6 

1-2  X  IO8 

"     hard  drawn    .    .    . 

70.2  Cu  +  29.8  Zn  .    .    .    . 

I2.I6 

- 

"      annealed    .    .    ,    . 

14-35 

— 

— 

3 

German  silver     .... 

Various     

2 

C  6o.i6Cu-f  25.37  Zn-f 

«... 

}  1  4.03  Ni  +  -30  Fe  with  trace 
(  of  cobalt  and  manganese  . 

3-33 

360 

— 

4 

Aluminum  bronze   .    .    . 

- 

7.5-8.5 

5-7Xio2 

- 

2 

Phosphor  bronze     .    .    . 

-  .        . 

10-20 

- 

- 

2 

Silicium  bronze  .... 

-       .     -  . 

41 

-     - 

- 

5 

Manganese-copper  .    .    . 

3oMn-}~7oCu  .    .    .  -.    .- 

I.OO 

AQ 

Nickel-manganese-copper 

2.IO 

—30 

- 

4 

Nickelin     

(  18.46  Ni  +  61.63  Cu  + 
]  19.67  Zn  -j-  0-24  Fe  -f 
(  0.19  Co  -f  o.iSMn    .    .     . 

3-01 

300 

- 

4 

Patent  nickel  ..... 

I  25.1  Ni  +  74-41  Cu+  . 
<  0.42  Fe  -f  0.23  Zn  -f 
(0.13  Mn  -f  trace  of  cobalt 

2.92 

190 

- 

4 

(  53.28  Cu  +  25.31  Ni  + 
<  16  89  Zn  pf«  4.46  Fe  +  » 

I  OO 

4IO 

i.yw 

Copper-manganese-iron    . 

91  Cu  +  7-1  Mn  +  1.9  Fe     . 
70.6  Cu  -f  23.2  Mn  -f  6.2  Fe 

4.98 
1-30 

1  2O 
22 

- 

6 
6 

M                        «                    U 

69.7  Cu  +  29.9  Ni  -f  0.3  Fe    . 

2.60 

120 

- 

7 

84  Cu  -f-  12  Mn  +  4  Ni 

2  1 

••J 

2  O4. 

18 

g 

l  Matthiessen.         8  W.  Siemens.                         6  Van  der  Ven.         6  Feussner. 

2  Various.               4  Feussner  and  Lindeck.        *  Blood.                    7  Jaeger-Diesselhorst. 

SMITHSONIAN  TABLES. 


TABLE  274. 
CONDUCTING  POWER  OF  ALLOYS. 


267 


The 


This  table  shows  the  conducting  power  of  alloys  and  the  variation  of  the  conducting  power  with  temperature.* 
values  of  C0  were  obtained  from  the  original  results  by  assuming  silver  =  —  g-  mhos.    The  conductivity  is  taken 

as  Ct=  C0  (i—at+W),  and  the  range  of  temperature  was  from  o°  to  100°  C. 

The  table  is  arranged  in  three  groups  to  show  (i)  that  certain  metals  when  melted  together  produce  a  solution 
which  has  a  conductivity  equal  to  the  mean  of  the  conductivities  of  the  components,  (2)  the  behavior  of  those 
metals  alloyed  with  others,  and  (3)  the  behavior  of  the  other  metals  alloyed  together. 

It  is  pointed  out  that,  with  a  few  exceptions,  the  percentage  variation  between  o°  and  100°  can  be  calculated  from  the 

formula  P  —  Pe  -f  where/  is  the  observed  and  V  the  calculated  conducting  power  of  the  mixture  at  100°  C, 
and  Pe  is  the  calculated  mean  variation  of  the  metals  mixed. 


Weight  % 

Vo  lume  % 

Variation  per  100°  C. 

Alloys. 

of  first  named. 

10* 

Observed. 

Calculated. 

GROUP  i. 

Sn6Pb    

77.O4 

83.96 

7.C7 

^800 

8670 

30.18 

29.67 

Sn4Cd   

82.41 
78.06 

83.10 
77.71 

9.18 
10.56 

4080 
3880 

11870 
8720 

28.89 
30.12 

30.03 
30.16 

SnZn     

PbSn     

64.13 
24.76 

53-41 

6.40 
16.16 

3780 
3780 

8420 
8000 

29.41 
29.86 

29.10 
29.67 

ZnCd2  f    

SnCd4   

23.05 
7-37 

23.50 
10-57 

13.67 
5.78 

3850 
3500 

9410 
7270 

29.08 
27.74 

30.25 
27.60 

CdPb6  

GROUP  2. 

Lead-silver  (Pb20Ag)  . 

95-05 

94.64 

c.6o 

3630 

7960 

28.24 

19.96 

Lead-silver  (PbAg)      . 
Lead-silver  (PbAg2)    . 

48.97 
32-44 

46.90 
30.64 

8.03 
13.80 

1990 

3100 
2600 

16.53 
I7-36 

7-73 
10.42 

Tin-gold  (Sn12Au)  .     . 

77-94 

90.32 

5-20 

3080 

6640 

24.20 

14.83 

"      "     (Sn6Au)    .    . 

59-54 

79-54 

3-03 

2920 

6300 

22.90 

5-95 

Tin-copper     .         .    . 

92.24 
80.58 

93-57 
83.60 

7-59 
8.05 

3680 
3330 

8130 
6840 

28.71 
26.24 

19.76 
14-57 

«       t. 
"       t. 

"       t. 

12.49 
10.30 
9.67 

14.91 

12.35 
1  1.  61 

5-57 
6.41 
7.64 

547 
666 
691 

294 
1185 
3°4 

5.18 
5-48 
6.60 

3-99 
4.46 
5-22 

«        «       -i- 

4.96 

6.O2 

12.44 

995 

70S 

9-25 

7-83 

^S 

1.41 

39-41 

2670 

5070 

21-74 

20.53 

Tin-silver  .    .    .    .    . 

91.30 
53-85 

96.52 

75-Si 

7.81 
8.65 

3820 
3770 

8190  e 
8550 

30.00 
29.18 

23-31 
11.89 

Zinc-copper  t     .    .    • 

36.70 

42.06 

13-75 

1370 

1340 

12.40 

11.29 

25.00 
l6-53 

29-45 
23.61 

13.70 
13-44 

1270 
1880 

1240 
1800 

11.49 
1  2.80 

10.08 
12.30 

«        ««       -j- 
«        «<       -i- 

8.89 
4.06 

10.88 
5-°3 

29.61 
38-09 

2040 
2470 

3030 
4100 

17.41 

20.61 

17.42 
20.62 

NOTE.  —  Barus,  in  the  "  Am.  Jour,  of  Sci."  vol.  36,  has  pointed  out  that  the  temperature  variation  of  platinum 
alloys  containing  less  than  10%  of  the  other  metal  can  be  nearly  expressed  by  an  equation  y  —  — —  m,  where  y  is  the 

temperature  coefficient  and  x  the  specific  resistance,  m  and  n  being  constants.     If  a  be  the  temperature  coefficient  at 
o°  C.  and  J  the  corresponding  specific  resistance,  s  (a  -f-  m)  =  n. 

For  platinum  alloys  Barus's  experiments  gave  m—  —  .000194  and  »  — .0378. 

For  steel  m  =  — .000303  and  n  =  .0620. 
Matthiessen's  experiments  reduced  by  Barus  gave  for 

Gold  alloys  m  =  —  .000045,  *=  .00721. 


= —  .000112,  »=:  .00538. 
Copper  "     m  =  —  .000386,  n  =  .00055. 

*  From  the  experiments  of  Matthiessen  and  Vogt, 
t  Hard-drawn. 


'  PhiL  Trans.  R.  S."  Y.  154. 


SMITHSONIAN  TABLES. 


268 


TABLE  274  (continued). 
CONDUCTING   POWER   OF   ALLOYS. 


GROUP  3. 

Alloys. 

Weight  % 

Volume  % 

,% 

,x,. 

,x.. 

Variation  per  100°  C. 

of  first  named. 

Observed. 

Calculated. 

Gold-copper  t     .    .    . 

99-23 

98.36 

35.42 

2650 

4650 

21.87 

23.22 

t*                **              -f 

90-55 

81.66 

10.16 

749 

81 

7.41 

7-53 

Gold-silver  t       ... 
"        "      * 

87.95 
87.95 

79.86 
79.86 

13.46 
13.61 

1090 
1140 

793 
1160 

10.09 
IO.2I 

9-65 

9-59 

«                «            4- 

64.80 

52.08 

9.48 

673 

246 

6.49 

6.58 

«                «           *             , 

r   «  f  •  •  • 

64.80 
3L33 

52.08 
19.86 

9.51 
13.69 

721 
885 

495 

6.71 
8.23 

6.42 
8.62 

"      *  .  .  . 

31.33 

19.86 

13-73 

908 

641 

8.44 

8.31 

Gold-copper  t     .    .    . 

34.83 

19.17 

12.94 

864 

570 

8.07 

8.18 

"         "      t     .    .    . 

1.52 

0.71 

53-02 

3320 

7300 

25.90 

25.86 

Platinum-silver  t     •    • 

U                      ((          4- 

33-33 
9.81 

19.65 
5-05 

4.22 
11.38 

330 

774 

208 
656 

3-io 

7.08 

3.21 

7-25 

"          t        '.        '. 

5-00 

2.51 

19.96 

1240 

1150 

11.29 

11.88 

Palladium-silver  t  •    • 

25.00 

23.28 

5-38 

324 

154 

3-40 

4.21 

Copper-silver  t        •    . 

98.08 

98.35 

56.49 

3450 

7990 

26.50 

27.30 

"     t        .    . 

94.40 

95-17 

51-93 

3250 

6940 

25.57 

25.41 

K         «     4. 

76.74 

77.64 

44.06 

3°3° 

6070 

24.29 

21.92 

«         «     4- 

42.75 

46.67 

47-29 

2870 

5280 

22.75 

24.00 

if               «         4- 

7.14 

8.25 

50-65 

2750 

4360 

23.17 

25-57 

«              «        4- 

50-30 

4120 

8740 

26.51 

29.77 

Iron-gold  t               •    • 
«       «    + 

13.59 
9.80 

27-93 
21.  18 

1:7J 

3490 
2970 

7010 
1  220 

27.92 

14.70 
1  1.  20 

"       "    t     .         .    • 

4.76 

10.96 

1.46 

487 

103 

3-84 

13.40 

Iron-copper  t      •    .    • 

0.40 

0.46 

24.51 

1550 

2090 

13.44 

14.03 

Phosphorus-copper  t  • 

2.50 

- 

4.62 

476 

145 

_ 

_ 

t  • 

0-95 

— 

14.91 

1320  - 

1640 

— 

— 

Arsenic-copper  t     •    . 

«                 tt            4- 

5-40 
2.80 

- 

3-97 

8.12 

736 

989 

446 

- 

- 

«                 «            -j- 

trace 

" 

38-52 

2640 

4830 

" 

*  Annealed. 
SMITHSONIAN  TABLES. 


t  Hard-drawn. 


TABLE  275.  269 

ELECTRICAL    RESISTANCE   OF  STRAIGHT  WIRES    WITH    ALTERNATING 
CURRENTS  OF  DIFFERENT  FREQUENCIES. 

This  table  gives  the  ratio  of  the  resistance  of  straight  copper  wires  with  alternating  currents  of 
different  frequencies  to  the  value  of  the  resistance  with  direct  currents. 


Diameter  of 
wire  in 
millimeters. 

Frequency  n  = 

60 

100 

1000 

IOOOO 

tooooo 

I  OOOOOO 

0.05 

_ 

_ 

_ 

_ 

_ 

*I.OOI 

O.I 

- 

- 

- 

- 

*I.OOI 

i.  008 

0.25 

— 

— 

— 

— 

1.003 

1.247 

- 

- 

- 

*I.OOI 

1.047 

2.240 

I.O 

2 

** 

~ 

I.OOI 

1.008 
1.  120 

1.503 
2.756 

4.19 

3 

— 

— 

1.  006 

1-437 

4.00 

4 

— 

— 

1.  02  1 

1.842 

5 

- 

*I.OOI 

1.047 

2.240 

7-5 

I.OOI 

1.002 

I.2IO 

3.22 

10 

15 

1.003 
1.  010 

1.008 
1.038 

I-503 
2.136 

4.19 

20 

1.044 

1.  120 

2.756 

25 

1.105 

1.247 

3'38 

40 

1.474 

1.842 

100 

4.19 

Values  between  i.ooo  and  i.ooi  are  indicated  by  *i.ooi. 

The  change  of  resistance  of  wires  other  than  copper  (iron  wires  excepted)  may  be  calculated 
from  the  above  table,  making  use  of  the  fact  that  the  change  of  resistance  is  a  function  of  the 
argument  /  =  2irrJ2n\  where  r  =  radius  of  cross-section,  «  =  frequency,  X  =  conductivity. 

If  a  given  wire  be  wound  into  a  solenoid,  its  resistance,  at  a  given  frequency,  will  be  greater  than 
the  values  in  the  table,  which  apply  to  straight  wires  only.  The  resistance  in  this  case  is  a  com- 
plicated function  of  the  pitch  and  radius  of  the  winding,  the  frequency,  and  the  diameter  of  the 
wire,  and  is  found  by  experiment  to  be  sometimes  as  much  as  twice  the  value  for  a  straight  wire. 

SMITHSONIAN  TABLES. 


270 


TABLE  276. 


INTERNATIONAL   ATOMIC  WEIGHTS    AND    ELECTROCHEMICAL   EQUIVA- 
LENTS. 

The  International  Atomic  Weights  are  quoted  from  the  report  of  the  International  Committee 
on  Atomic  Weights  ("Jour.  Am.  Chem.  Soc.,"  vol.  32,  p.  3,  1910). 

With  the  exception  of  the  value  given  for  silver  and  that  corresponding  to  valence  2  for  copper, 
the  electrochemical  equivalents  given  in  this  table  have  been  calculated  from  the  atomic  weights 
and  one  or  two  of  the  more  common  apparent  valences  of  th«  substance.  The  value  given  for 
silver  is  that  which  was  adopted  by  the  International  Congress  of  Electricians  at  Chicago  in  1894. 


Substance. 

Symbol. 

Relative 
atomic  wt. 
Oxygen  =  16. 

Relative 
atomic  wt. 
Hydrogen  =  i. 

Valence. 

Electrochemical 
equivalent  in  grammes 
per  coulomb  X  1000. 

Al 

Sb 

A 
As 

H 

Ba 
Bi 

H 

B 
Br 

Cd 
Cs 
Ca 
C 
Ce 

Cl 

Cr 

« 

Co 
« 

Cb 

Cu 
« 

& 

Eu 
F 
Gd 
Ga 
Ge 

Gl 

Au 
He 
H 
In 

I 
Ir 

Fe 
« 

Kr 

La 

Pb 
Li 
Lu 

Mg 

Mn 
« 

27.1 
120.2 

39-9 
74.96 

137-37 
208.0 

M 

II.O 

79.92 

112.40 

132.81 
40.09 

12.00 
140.25 

3546 
52.0 
« 

58-97 

93-5 
63.57 

162.5 
167.4 

152.0 
19.0 

'£•3 

69.9 
72.5 

9.1 

197.2 
4.o 
i.  008 
114.8 

126.92 
i93-i 

55;85 

83.0 

139.0 
207.10 
7.00 
174.0 
24.32 
54-93 

26.9 
II9-3 

39-6 
744 

136.27 

206.3 

(i 

10.9 

79.28 

111.51 

131.76 

39-77 
11.99 

I39-H 

35-^9 
51.6 

58.50 

92.8 
63.07 

161.2 
166.1 

150.8 
18.9 

'I!'1 
69.3 

71-9 

9-03 
195-7 
4.0 

1.  000 

"3-9 

125.91 
191.6 
55;4i 

82.4 

137.9 
205.46 
6.94 
172.6 
24.13 

5449 
« 

3 
3 

5 

3 

5 

2 

3 

5 
3 

i 

2 
I 
2 

4 

2 

I 

I 

2 

3 

5 

i 

2 
2 

I 

3 

2 

3 

i 
3 

r 
4 

2 

3 

2 
2 
I 

2 
2 
4 

.0936 
.4152 
.2491 

.2590 
•1554 

.7118 

.7185 

43" 

.0380 
.8282 

0.5824 

1-3764 
0.2077 

•0313 
.7267 

•3675 
.1797 
.0900 
.3061 
.2041 

:$i 

.3290 
.8624 

.1968 
.2414 

.0471 
.6818 

.0104 
0.3966 

i-3i53 
0.5003 
.2894 
.1929 

0.7202 
1.0731 
0.0725 

.1260 
.2846 
.1423 

« 

Argon                      . 

Bismuth    

u 

Boron    

Caesium          .          .     •     . 

Carbon      

Cerium      •••••• 

Chlorine    •••••* 

« 

Cobalt  

« 

Columbium   

« 

Dysprosium  

Erbium      .     .     .     .     . 

Europium      .     .    .    .     . 

Gallium          .    •     •    •    • 

Germanium        •     •    •    . 

Gold     

Indium  ....... 

« 

Lead                   .... 

Magnesium         .... 

<« 

SMITHSONIAN  TABLES. 


TABLE  276  (continued).  2JI 

INTERNATIONAL   ATOMIC   WEIGHTS   AND   ELECTROCHEMICAL   EQUIVA- 
LENTS. 


Substance. 

Symbol. 

Relative 
atomic  wt. 
Oxygen  r=i6. 

Relative 
atomic  wt. 
Hydrogens  i. 

Valence. 

Electrochemical 
equivalent  in  grammes 
per  coulomb  X  1000. 

Mercury  
« 

Hg 

200.0 
«< 

198.5 

I 
2 

2.0727 
1.0363 

Molybdenum     .... 
Neodymium  .    .         . 

Mo 

Nd 

96.0 
144.  i 

95-3 

14-5.2 

6 

0.1658 

Neon    

Ne 

2O.O 

IQ.Q 

_ 

_ 

Nickel  

Ni 

58.68 

<8.21 

2 

.7O4O 

<t 

•3 

.2O27 

Nitrogen  ...         .    . 

N 

I4.OI 

I7.QO 

-3 

.04.84 

« 

it 

H 

e 

O2QO 

Os 

I9O.9 

l89.4 

I 

.-I2Q7 

Oxygen     

o 

16.00 

15.88 

2 

.0829 

Palladium      .          ... 

Pd 

I  O6.7 

ICK.Q 

2 

.CC28 

« 

it 

W 

.2211 

Phosphorus       .... 
« 

P 
« 

Pt 

31.0 
iqc.O 

30.8 
IQ^.4 

3 

5 

2 

.1071 
0.0642 

I.OIO4 

el 

« 

H 

O  <XX2 

Potassium     .     .     .     .     . 

K 

"3Q.IO 

-18.70 

I 

.4OC2 

Praesodymium  .... 

Pr 
Rd 

jy.iw 

140.6 
226.4 

!39-S 
224.6 

Rh 

IO2.Q 

IO2.I 

.•JCC4 

Rubidium     .     .    .     . 

Rb 

8c  41: 

8477 

I 

8855 

Ru 

101.7 

IOO.Q 

4 

,26^«; 

Sa 

I  en  A 

I4Q  2 

Scandium      ..... 

Sc 

44.  I 

4-5.7 

Se 

70.2 

78.6 

2 

.4104 

Si 

28.3 

28.2 

4 

0.07^  7 

Silver  

As 

107.88 

IO7.O2 

I 

1.1180 

Sodium         

si 

23.00 

22.82 

I 

0.2^84 

Strontium     .    .    • 

Sr 

8762 

8692 

2 

.41:40 

s 

•32.07 

31.82 

2 

.1662 

Tantalum      

Ta 
Te 

l8l.O 
127.  C 

179.6 
126.5 

5 

2 

oiile 

Terbium  ...... 

Tb 

ICQ  2 

1  17  O 

Tl 

204.0 

2O2.4. 

_ 

2.1141 

Thorium  

Th 

2^2.42 

27O.  «J7 

2 

I.2O43 

Thulium  

Tm 

i68.c 

167.2 

Tin  

Sn 

IIQ.O 

118.1 

2 

0.6166 

<t 

«i 

V 

« 

4' 

•3083 

Titanium  

Ti 

48  i 

47.7 

.124.6 

W 

184. 

183. 

6 

O,7I78 

u 

238.5" 

236.6 

2 

t.2V& 

<« 

ti 

•} 

oj°o 

0.8238 

Vanadium    ..... 

v 

ei  2 

CQ.8 

•3 

,1700 

«i 

« 

50.0 

5" 

.1061 

Xe 

I-5Q.7 

I2Q.7 

Yb 

172.0 

*i.y./ 

170  6 

Yttrium    

Yt 

8o.O 

883 

2 

.4611 

Zinc     

Zn 

•pr** 

6c  77 

64.88 

2 

.•j-?8^ 

Zr 

j,  -ji 

QO.6 

8q.Q 

4 

.2-347 

SMITHSONIAN  TABLES. 


2/2  TABLES  277,  278. 

CONDUCTIVITY  OF   ELECTROLYTIC  SOLUTIONS. 

This  subject  has  occupied  the  attention  of  a  considerable  number  of  eminent  workers  in 
molecular  physics,  and  a  few  results  are  here  tabulated.  It  has  seemed  better  to  confine  the 
examples  to  the  work  of  one  experimenter,  and  the  tables  are  quoted  from  a  paper  by  F.  Kohl- 
rausch,*  who  has  been  one  of  the  most  reliable  and  successful  workers  in  this  field. 

The  study  of  electrolytic  conductivity,  especially  in  the  case  of  very  dilute  solutions,  has  fur- 
nished material  for  generalizations,  which  may  to  some  extent  help  in  the  formation  of  a  sound 
theory  of  the  mechanism  of  such  conduction.  If  the  solutions  are  made  such  that  per  unit 
volume  of  the  solvent  medium  there  are  contained  amounts  of  the  salt  proportional  to  its  electro- 
chemical equivalent,  some  simple  relations  become  apparent.  The  solutions  used  by  Kohlrausch 
were  therefore  made  by  taking  numbers  of  grammes  of  the  pure  salts  proportional  to  their  elec- 
trochemical equivalent,  and  using  a  litre  of  water  as  the  standard  quantity  of  the  solvent.  Tak- 
ing the  electrochemical  equivalent  number  as  the  chemical  equivalent  or  atomic  weight  divided 
by  the  valence,  and  using  this  number  of  grammes  to  the  litre  of  water,  we  get  what  is  called 
the  normal  or  gramme  molecule  per  litre  solution.  In  the  table,  m  is  used  to  represent  the 
number  of  gramme  molecules  to  the  litre  of  water  in  the  solution  for  which  the  conductivities 
are  tabulated.  The  conductivities  were  obtained  by  measuring  the  resistance  of  a  cell  filled  with 
the  solution  by  means  of  a  Wheatstone  bridge  alternating  current  and  telephone  arrangement. 
The  results  are  for  18°  C.,  and  relative  to  mercury  at  o°  C.,  the  cell  having  been  standardized  by 
filling  with  mercury  and  measuring  the  resistance.  They  are  supposed  to  be  accurate  to  within 
one  per  cent  of  the  true  value. 

The  tabular  numbers  were  obtained  from  the  measurements  in  the  following  manner  :  — 

Let  A"18  =  conductivity  of  the  solution  at  18°  C.  relative  to  mercury  at  o°  C. 

JC?%  =  conductivity  of  the  solvent  water  at  18°  C.  relative  to  mercury  at  o°  C. 

Then  -AT18  — A^8  =  £18  =  conductivity  of  the  electrolyte  in  the  solution  measured. 

-^  =  /*  =  conductivity  of  the  electrolyte  in  the  solution  per  molecule,  or  the  "  specific 
molecular  conductivity." 


TABLE  277.— Value  of  fc18  for  a  few  Electrolytes. 

This  short  table  illustrates  the  apparent  law  that  the  conductivity  in  very  dilute  solutions  is  proportional  to  the 

amount  of  salt  dissolved. 


M 

KC1 

NaCl 

AgN03 

KC2HS0, 

K2S04 

MgS04 

O.OOOOOI 

i.  216 

1.024 

1.  080 

0-939 

1.275 

1.056 

O.OOOO2 
0.00006 

2-434 
7.272 

2.056 
6.162 

2.146 
6.462 

5.610 

2.532 
7-524 

2.104 

6.216 

O.OOOI 

12.09 

10.29 

10.78 

9-34 

12.49 

10.34 

TABLE  278. -Electro-Chemical  Equivalents  and  Normal  Solutions. 

The  following  table  of  the  electro-chemical  equivalent  numbers  and  the  densities  of  approximately  normal  solutions 
of  the  salts  quoted  in  Table  271  may  be  convenient.  They  represent  grammes  per  cubic  centimetre  of  the  solution 
at  the  temperature  given. 


Salt  dissolved. 

Grammes 
per  litre. 

« 

Temp. 
C. 

Density. 

S 

alt  dissolved. 

Grammes 
per  litre. 

m 

Temp. 
C. 

Density. 

KC1    . 
NH4C1 
NaCl  . 
LiCl    . 

74-59 
53-55 
58.50 
42.48 

I.O 

1.0009 

I.O 
I.O 

1^.2 
18.6 
18.4 
18.4 

1.0457 
1.0152 
1.0391 
1.0227 

Na2SO4 
Li2S04 

87.16 
71.09 

55.09 
60.17 

I.O 
1.0003 
1.0007 
1.0023 

q\vqvovo 
odod  odod 

1.0658 
1.0002 
1.0445 
1.0573 

JBaCl2 

104.0 

I.O 

18.6 

1.0888 

rZnSO4 

80.58 

I.O 

5-3 

1.0794 

^ZnCl2 

68.0 

I.OI2 

15.0 

1.0592 

^CuSO4 

79-9 

I.OOI 

18.2 

1.0776 

KT 

165.9 

I.O 

1  8.6 

1.1183 

K2CO3 

69.17 

1.  0006 

18.3 

1.0576 

KNO8 

101.17 

I.O 

18.6 

I.  O6oi 

Na^COs 

53-04 

I.O 

17.9 

1.0517 

NaNO8 

85.08 

I.O 

18.7 

1.0542 

ECOH    . 

56.27 

1.0025 

18.8 

1.0477 

AgN08 
iBa(N08)2 
KC1O8     . 
KC2H8O2 

169.9 
65.28 
61.29 
98.18 

I.O 

o'-5 
1.0005 

18.3 
18.6 

1.0367 
1.0467 

] 
] 
i 

flci    . 

;H2SO4 

36.51 
63.13 
49.06 

I.004I 
I.OOI4 
1.  0006 

18.6 
18.6 
18.9 

1.0161 
1.0318 
1.0300 

SMITHSONIAN  TABLES. 


*  "  Wied.  Ann."  vol.  a6,  pp.  i6z-w6. 


TABLE  279.  273 

SPECIFIC   MOLECULAR   CONDUCTIVITY  /x  :  MERCURY  =  1O8. 


Salt  dissolved. 

m—  10 

5 

3 

i 

0.5 

O.I 

.05 

.03 

JOH 

iK2S04  . 

_ 

_ 

_ 

_ 

672 

736 

897 

959 

1098 

tea 

_ 

_ 

827 

919 

958 

1047 

1083 

1107 

"47 

KI.           . 

- 

770 

968 

997 

1069 

1  102 

1123 

1161 

NH4C1     . 
KN08      . 

- 

752 

572 

907 

752 

948 
839 

I035 
983 

1078 
1037 

IIOI 

1067 

1142 

1122 

^BaCl2     . 

- 

_ 

487 

658 

725 

861 

904 

939 

IOO6 

KC1O3     . 

— 

— 

— 

799 

927 

(976) 

1006 

I053 

£Ba2N2O6 

- 

- 

- 

- 

755 

828 

(870) 

• 

^CuSO4  .        .        . 

— 

— 

J5° 

241 

288 

424 

479 

537 

675 

AgN03    .        .   ,.  . 

- 

351 

448 

635 

728 

886 

936 

(966) 

1017 

ZnSO4  . 

_ 

82 

146 

249 

302 

43  i 

500 

556 

685 

MgSO4  .        . 

— 

82 

I5I 

270 

330 

474 

532 

587 

715 

-Na2SO4 

_ 

_ 

__ 

475 

784 

828 

906 

] 

ZnCl2     . 
NaCl 

60 

180 
398 

280 
528 

§1 

757 

865 

851 
(920) 

9625 

NaNO3    . 

_ 

_ 

43° 

617 

694 

817 

855 

877 

907 

KC2H302 

30 

240 

38i 

594 

671 

784 

820 

841 

879 

1    j 

-nSo?3    :    : 

660 

1270 

254 
1560 

427 
1820 

510 
1899 

682 
2084 

2343 

799 
2515 

899 
2855 

i 

:2H4o   i      .      . 

°-5 

2.6 

5-2 

12 

19 

43 

62 

79 

132 

HC1         ... 

600 

1420 

2OIO 

2780 

3017 

3244 

333° 

3369 

34i6 

HNO3     . 

610 

1470 

2070 

2770 

2991 

3225 

3289 

3328 

3395 

] 

rH3P04  .        .        . 
<.OH       . 

148 
423 

160 
990 

170 

200 
I7l8 

250 
1841 

43° 
1986 

540 
2045 

620 

2078 

790 
2124 

NH3 

2.4 

3-3 

8.4 

12 

3i 

43 

50 

92 

Salt  dissolved. 

.006 

.002 

.001 

.0006 

.0002 

.0001 

.00006 

.00002 

.00001 

|K2S04    . 
KC1         ... 

1130 
1162 

1181 
"85 

1207 
"93 

1  220 
"99 

1241 
I2O9 

1249 
1209 

1254 

1212 

1266 
1217 

1275 

1216 

KI  . 

1176 

"97 

1203 

1209 

1214 

1216 

1216 

1216 

1207 

NH4C1    . 

"57 

1180 

1190 

"97 

1204 

1209 

1215 

1209 

1205 

KN03     . 

1140 

"73 

1180 

1190 

"99 

1207 

1220 

1198 

1215 

j 

BaCl2     . 
CC1O3     . 

1031 
1068 

1074 
1091 

1092 

IIOI 

IIO2 
1109 

1118 
1119 

1126 

1122 

"33 
1126 

"44 

"35 

1142 
II4I 

'Ba2N2Oe        «        . 

982 

I033 

1054 

1066 

1084 

1096 

IIOO 

1114 

III4 

1 

CuS04  . 

740 

873 

95° 

987 

1039 

1062 

1074 

1084 

1086 

i 

VgNO3    . 

I033 

1057 

1068 

1069 

1077 

1078 

1077 

1073 

1080 

ZnSO4  . 
-MgS04  .        .        . 
Na2SO4 

744 
773 
933 

861 

881 
980 

919 

w 

1009 

1001 

1015 
1026 

IO23 
1034 
1034 

1032 

1036 
1038 

1047 
1052 
1056 

1060 
1056 

1054 

\ 

ZnCl2     . 

939 

979 

994 

1004 

1  020 

IO29 

1031 

1035 

1036 

'- 

STaCl 

976 

998 

1008 

1014 

1018 

IO29 

1027 

1028 

IO24 

NaN08   . 

921 

942 

952 

956 

966 

975 

970 

972 

975 

KC2H3O2 

891 

913 

919 

923 

933 

934 

935 

943 

939* 

\ 

Na2CO3 

956 

IOIO 

1037 

1046 

988 

874 

790 

715 

\ 

H2SO4  . 

3001 

3240 

33J6 

3342 

3280 

3118 

2927 

2077 

1413* 

C2H4O    . 

170 

283 

380 

470 

796 

995 

"33 

1328 

1304* 

HC1 

3438 

3455 

3455 

3440 

3340 

3*70 

2968 

2057 

1254* 

HNO3     . 

3448 

3427 

3408 

3285 

3088 

2863 

1904 

"44* 

! 

H3P04  .        .        . 
COH       . 

858 
2141 

945 
2140 

968 

2110 

977 
2074 

920 
1892 

1689 

746 
1474 

497 
845 

402* 
747* 

NH3 

116 

190 

260 

330 

500 

610 

690 

700 

560* 

Acids  and  alkaline  salts  show  peculiar  irregularities. 


SMITHSONIAN  TABLES. 


274  TABLES  280,  281 . 

LIMITING  VALUES  OF  fL.    TEMPERATURE  COEFFICIENTS. 

TABLE  280.  —  Limiting  Values  of  p. 
This  table  shows  limiting  values  of  ft  =  —  .  lo8  for  infinite  dilution  for  neutral  salts,  calculated  from  Table  271. 

fft 


Salt. 

/* 

Salt. 

P 

Salt. 

/* 

Salt. 

H 

*K2SO4     . 

1280 

iBaC!2       . 

1150 

}MgS04    . 

1080 

}H2S04    . 

3700 

KC1  .    *   :^ 

I22O 

iKC108     . 

1150 

iNa2SO4  . 

1060 

HC1      .    . 

3500 

KI    .    .    . 

1220 

iBaN206  . 

II2O 

|ZnCl    .    . 

1040 

HN08.    . 

3500 

NH4C1.    . 

I2IO 

iCuSO4    . 

1  100 

NaCl     .    . 

1030 

£H8P04    . 

IIOO 

KN08  .    . 

1210 

AgN08     . 

lOQO 

NaN03     . 

980 

KOH   .    . 

2200 

- 

- 

iZnSO4    . 

I080 

K2C2H8O2 

940 

|Na2C08  . 

1400 

If  the  quantities  in  Table  271  be  represented  by  curves,  it  appears  that  the  values  of  the 
specific  molecular  conductivities  tend  toward  a  limiting  value  as  the  solution  is  made 
more  and  more  dilute.  Although  these  values  are  of  the  same  order  of  magnitude,  they 
are  not  equal,  but  depend  on  the  nature  of  both  the  ions  forming  the  electrolyte. 

When  the  numbers  in  Table  272  are  multiplied  by  Hittorf's  constant,  or  o.ooon,  quan- 
tities ranging  between  0.14  and  o.i o  are  obtained  which  represent  the  velocities  in  milli- 
metres per  second  of  the  ions  when  the  electromotive  force  gradient  is  one  volt  per 
millimetre. 

Specific  molecular  'conductivities  in  general  become  less  as  the  concentration  is  in- 
creased, which  may  be  due  to  mutual  interference.  The  decrease  is  not  the  same  for 
different  salts,  but  becomes  much  more  rapid  in  salts  of  high  valence. 

Salts  having  acid  or  alkaline  reactions  show  marked  differences.  They  have  small 
specific  molecular  conductivity  in  very  dilute  solutions,  but  as  the  concentration  is  in- 
creased the  conductivity  rises,  reaches  a  maximum  and  again  falls  off.  Kohlrausch  does 
not  believe  that  this  can  be  explained  by  impurities.  HsPO4  in  dilute  solution  seems  to 
approach  a  monobasic  acid,  while  H2SO4  shows  two  maxima,  and  like  H8PO4  approaches 
in  very  weak  solution  to  a  monobasic  acid. 

Kohlrausch  concludes  that  the  law  of  independent  migration  of  the  ions  in  media  like 
water  is  sustained. 


TABLE  281. -Temperature  Coefficients. 

The  temperature  coefficient  in  general  diminishes  with  dilution,  and  for  very  dilute  solutions  appears  to  approach  a 
common  value.  The  following  table  gives  the  temperature  coefficient  for  solutions  containing  o.oi  gramme  mole- 
cule of  the  salt. 


Salt. 

Temp. 
Coeff. 

Salt. 

Temp. 
Coeff. 

Salt. 

Temp. 
Coeff. 

Salt. 

Temp. 
Coeff. 

KC1  .    .    . 

0.0221 

KI    .    .    . 

0.0219 

iK2S04      . 

0.0223 

*K2C08    .    . 

0.0249 

NH4C1.    . 
NaCl     .    . 
LiCl.    .    . 

iZnCla  .    . 
iMgCla      . 

0.0226 
0.0238 
0.0232 
0.0234 
0.0239 
0.0241 

KN08  .    . 
NaNO8.    . 
AgN08.    . 
iBa(N08)2 
KC108  .    . 
KC2H8Oa  . 

0.02  1  6 
O.O226 
O.022I 
0.0224 
O.O2I9 
0.0229 

|NasSO4    . 

|MgS04     . 
iZnSO8     . 
iCuSO4     . 

0.0240 
0.0242 
0.0236 
0.0234 
0.0229 

iNa2C08  .    . 

0.0265 

KOH    .    .    . 
HC1      .    .    . 
HNO8  .    .    . 
iH2S04     .    . 

0.0194 

o.oi  59 

O.OI  O2 

0.0125 

|H2S04         ) 
for  m  =  .001  ( 

0.0159 

SMITHSONIAN  TABLES. 


TABLE  282. 


275 
BASES    IN 


THE    EQUIVALENT    CONDUCTIVITY    OF    SALTS,    ACIDS  AND 

AQUEOUS  SOLUTIONS. 

In  the  following  table  the  equivalent  conductance  is  expressed  in  reciprocal  ohms.  The  con- 
centration is  expressed  in  milli-equivalents  of  solute  per  litre  of  solution  at  the  temperature  to  which 
the  conductance  refers.  (In  the  cases  of  potassium  hydrogen  sulphate  and  phosphoric  acid  the 
concentration  is  expressed  in  milli-formula-weights  of  solute,  KHSO*  or  HgPO^  per  litre  of  solu- 
tion, and  the  values  are  correspondingly  the  modal,  or  "  formal,"  conductances.)  Except  in  the 
cases  of  the  strong  acids  the  conductance  of  the  water  was  subtracted,  and  for  sodium  acetate, 
ammonium  acetate  and  ammonium  chloride  the  values  have  been  corrected  for  the  hydrolysis  of 
the  salts.  The  atomic  weights  used  were  those  of  the  International  Commission  for  1905,  referred 
to  oxygen  as  16.00.  Temperatures  are  on  the  hydrogen  gas  scale. 

Concentration  in 


Equivalent  conductance  in 


reciprocal  ohms  per  centimetre  cube 
gramme  equivalents  per  cubic  centimetre 


Substance. 

a  jj 

ji 

Equivalent  conductance  at  the  following  °  C  temperatures. 

18° 

25° 

50° 

75° 

100° 

128° 

156° 

218° 

281° 

3060 

Potassium  chloride 

0 

130.1 

(152.1) 

(232.5) 

(32L5) 

414 

(519) 

625 

825 

1005 

II2O 

"               " 

2 

126.3 

146.4 

- 

393 

588 

779 

930 

I008 

«                (i 

10 

122.4 

141.5 

215.2 

295.2 

377 

470 

560 

741 

874 

9IO 

" 

80 

"3-5 

•    — 

342 

— 

498 

638 

723 

720 

Sodium  chloride 

IOO 

o 

II2.0 

129.0 

194.5 

264.6 

362 

415 

490 

555 

760 

970 

I080 

" 

2 

105.6 

— 

— 

— 

349 

— 

534 

722 

895 

955 

«             a 

10 

IO2.O 

— 

— 

— 

336 

— 

511 

685 

820 

860 

u                 « 

80 

93-5 

- 

- 

- 

301 

- 

450 

500 

674 

680 

tt            « 

IOO 

92.0 

— 

— 

— 

296 

— 

442 

Silver  nitrate 

o 

115.8 

- 

- 

- 

367 

- 

570 

780 

965 

1065 

N 

2 

II2.2 

— 

— 

— 

353 

— 

539 

727 

877 

935 

" 

10 

I08.0 

— 

— 

— 

337 

— 

673 

790 

818 

" 

20 

IO5.I 

— 

— 

— 

326 

— 

488 

639 

" 

40 

IOI-3 

— 

_ 

— 

312 

— 

462 

599 

680 

680 

U 

80 
IOO 

96.5 

94.6 

— 

— 

— 

~ 

432 

552 

614 

604 

Sodium  acetate 

0 

78.! 

- 

- 

- 

285 

- 

45° 

660 

- 

924 

" 

2 

74-5 

— 

— 

— 

268 

— 

421 

578 

— 

801 

" 

10 

71.2 

— 

— 

— 

253 

— 

396 

542 

— 

702 

«           « 

80 

634 

— 

_ 

— 

221 

— 

340 

452 

Magnesium  sulphate 

o 

II4.I 

- 

- 

- 

426 

- 

690 

1080 

** 

2 

94-3 

-» 

— 

— 

302 

— 

377 

260 

" 

IO 

76.1 

— 

— 

— 

234 

— 

241 

'43 

m 

2O 
40 

67.5 
59-3 

_ 

— 

_ 

190 

160 

„ 

1 

no 

88 

" 

80 

52.0 

— 

— 

— 

136 

— 

75 

" 

IOO 

49.8 

- 

- 

- 

130 

- 

126 

" 

2OO 

43-  1 

— 

— 

— 

no 

— 

IOO 

Ammonium  chloride 

0 

131.1 

152.0 

- 

- 

(415) 

- 

(628) 

(841) 

. 

(1176) 

* 

2 

126.5 

146.5 

- 

- 

399 

- 

601 

801 

- 

1031 

10 

122.5 

141.7 

— 

— 

382 

— 

573 

758 

— 

925 

" 

3° 

118.1 

— 

_ 

— 

— 

— 

_ 

828 

Ammonium  acetate 

o 

(99.8) 

- 

- 

- 

(338) 

- 

(523) 

«                    u 

10 

91.7 

— 

— 

— 

300 

— 

456 

25 

88.2 

— 

f^ 

" 

286 

"** 

426 

From  the  investigations  of  Noyes,  Mclcher,  Cooper,  Eastman  and  Kato ;  Journal  of  the  American  Chemical  Society, 

30, 1908. 
SMITHSONIAN  TABLE*. 


276  TABLE  282  (continued). 

THE    EQUIVALENT    CONDUCTIVITY    OF    SALTS,    ACIDS    AND    BASES    IN 

AQUEOUS    SOLUTIONS. 


Substance. 

Concen-  I 
tration.  I 

Equivalent  conductance  at  the  following  °  C  temperatures. 

18° 

»5° 

50° 

75° 

100° 

1280 

i560 

218° 

*8iO 

3o60 

Barium  nitrate 

0 

116.9 

_ 

^ 

_ 

385 

mt 

600 

840 

1  120 

1300 

"          . 

2 

109.7 

— 

— 

— 

352 

— 

536 

715 

828 

824 

"          . 

10 

IOI.O 

— 

— 

— 

322 

— 

48l 

618 

658 

615 

" 

40 

88.7 

- 

- 

- 

280 

- 

412 

507 

503 

448 

"          . 

80 

81.6 

- 

- 

- 

258 

- 

372 

449 

430 

"          . 

IOO 

79.1 

— 

— 

— 

249 

Potassium  sulphate 

o 

2 

132-8 
124.8 

— 

— 

_ 

455 
402 

~ 

715 
605 

IS 

1460 

'S675 

" 

10 

115.7 

- 

- 

- 

365 

- 

537 

672 

68? 

637 

"         «  ! 

40 
80 

104.2 
97-2 

_ 

** 

_ 

320 
294 

"~ 

455 

31 

448 

466 
396 

«         «  t 

IOO 

95-o 

— 

— 

— 

286 

Hydrochloric  acid 

0 

379-o 

- 

- 

- 

850 

- 

1085 

1265 

1380 

1424 

«        !!  ; 

2 

10 

368^1 

~* 

""" 

T 

826 
807 

~" 

1048 
1016 

1168 

1332 
1226 

1337 
1162 

"             "  . 

80 

353-o 

- 

- 

- 

762 

- 

946 

1044 

1046 

862 

«             «  f 

IOO 

35°-6 

— 

— 

— 

754 

— 

929 

1006 

Nitric  acid 

0 

377-o 

421.0 

570 

706 

826 

945 

1047 

(1230) 

- 

(1380) 

«        <« 

2 

371.2 

4I3-7 

559 

690 

806 

919 

1012 

1166 

— 

1156 

«        « 

IO 

406.0 

548 

676 

786 

893 

978 

«        « 

50 

353-7 

393-3 

528 

649 

750 

845 

917 

«                (I                             ^ 

IOO 

346.4 

385-0 

5I6 

632 

728 

817 

880 

— 

— 

454* 

Sulphuric  acid 

o 

(429) 

(590 

(746) 

891 

(1041) 

1176 

1505 

- 

(2030) 

"         . 

2 

353-9 

390.8 

501 

561 

551 

536 

563 

— 

637 

«           i< 

10 

309.0 

337-o 

406 

435 

446 

460 

48l 

533 

«           u 

50 

253-5 

273-0 

323 

356 

384 

417 

448 

502 

«           «i 

IOO 

233-3 

251.2 

300 

336 

369 

404 

435 

483 

- 

474* 

Potassium  hydrogen  \ 
sulphate    .     .    .    ) 

2 

50 
IOO 

455-3 
295-5 
263.7 

506.0 

ig? 

661.0 

374-4 
329.1 

754 
403 
354 

784 
422 
375 

773 
446 

402 

754 
477 
435 

Phosphoric  acid    . 

0 

338.3 

376 

73° 

839 

93° 

«             «« 

2 

283.1 

401 

464 

498 

508 

489 

"            " 

IO 

203.0 

222.O 

273 

300 

308 

298 

274 

«            « 

50 

122.7 

132.6 

157.8 

1  68.6 

168 

158 

142 

" 

IOO 

96-5 

104.0 

122.7 

129.9 

128 

120 

1  08 

Acetic  acid 

o 

(347-0) 

- 

(773) 

- 

(980) 

[1165) 

- 

(1268) 

«        «              t 

10 

14.50 

— 

— 

— 

25.1 

— 

22.2 

14.7 

u        <« 

30 

8.50 

- 

- 

- 

14.7 

- 

I3.0 

8.65 

"        "              . 

80 

5-22 

— 

— 

— 

9-05 

— 

8.00 

5-34 

«        «              ^ 

IOO 

4-67 

— 

— 

— 

8.10 

— 

— 

4.82 

— 

'-57 

Sodium  hydroxide 

0 

216.5 

- 

- 

- 

594 

- 

835 

1060 

"               «       t 

2 

2I2.I 

— 

— 

— 

582 

— 

814 

"               " 

20 

205.8 

- 

- 

- 

559 

- 

77I 

93° 

Barium  hydroxide 

50 
O 

200.6 
222 

256 

389 

(520) 

as 

(760) 

847 

873 

"    .    . 

2 

2I5 

359 

4 

591 

"             "    .    t 

10 

207 

235 

342 

449 

548 

664 

722 

««             « 

50 

I9I.I 

2I5.I 

308 

399 

478 

549 

593 

f 

IOO 
0 

iSo.I 
(238) 

2O4.2 
(271) 

291 
(404) 

373 
(526) 

443 
(647) 

5°3 
(764) 

(9oS 

(1141) 

_ 

(1406) 

Ammonium  hydrox«  I 

10 

9.66 

- 

23.2 

22.3 

15.6 

ide  1 

30 

5.66 

_ 

^ 

— 

13.6 

<fc 

Il-O 

I 

IOO 

J.W 

3.10 

3-62 

5-35 

6.70 

O 

7-47 

^ 

O 

7.17 

4.82 

— 

i-33 

*  These  values  are  at  the  concentration  80,0, 


SMITHSONIAN  TABLES. 


TABLE  283. 


277 


THE    EQUIVALENT    CONDUCTIVITY    OF    SOME    ADDITIONAL    SALTS    IN 

AQUEOUS  SOLUTION. 

Conditions  similar  to  those  of  the  preceding  table  except  that  the  atomic  weights  for  1908  were  used. 


Substance. 

Concen- 
tration. 

Equivalent  conductance  at  the  following  °  C  temperature. 

0° 

18° 

25° 

50° 

75° 

100° 

128° 

156° 

Potassium  nitrate 

0 

80.8 

126.3 

145-1 

219 

299 

384 

485 

580 

"              " 

2 

78.6 

122.5 

140.7 

212.7 

289.9 

370.3 

460.7 

" 

12.5 

75-3 

II7.2 

134.9 

202.9 

276.4 

351.5 

435-4 

520.4 

" 

5° 

70.7 

109.7 

126.3 

189.5 

2574 

326.1 

402.9 

476.1 

«                         K 

IOO 

67.2 

104.5 

120.3 

180.2 

244.1 

308.5 

§5 

447-3 

Potassium  oxalate 

0 

2 

79-4 
74-9 

127.6 
119.9 

147.5 
139.2 

230 
215.9 

322 
3OO.2 

419 
389.3 

i 

ii              « 

12.5 

69-3 

III.  I 

129.2 

199.1 

275.1 

354.1 

8 

524.3 

<«              « 

50 

63 

101 

116.5 

178.6 

244.9 

312.2 

8 

449-5 

" 

IOO 
200 

81 

94.6 

109.5 

102.3 

155 

227.5 
2IO.9 

288.9 

265.1 

353-2 
321.9 

409-7 
372-1 

Calcium  nitrate 

0 

70.4 

II2.7 

130.6 

202 

282 

369 

474 

575 

« 

2 

12.5 

66.5 
61.6 

I07.I 

123.7 

"4-5 

I9I.9 
176.2 

266.7 
244 

346.5 
314.6 

438.4 
394-5 

529.8 
473-7 

«<           ii 

5° 

55-6 

88.6 

102.6 

157-2 

216.2 

276.8 

343 

405.1 

ii           « 

IOO 

82.6 

95-8 

146.1 

199.9 

255.5 

369.1 

«            «< 

200 

48.3 

76.7 

oo.o 

135-4 

184.7 

234-4 

288 

334-7 

Potassium  ferrocyanide 

0 

98.4 

159.6 

185.5 

288 

403 

527 

" 

0.5 

91.6 

171.1 

« 

2. 

84.8 

137 

158.9 

243-8 

335-2 

427.6 

" 

12.5 

71 

113.4 

131.6 

2OO.3 

27I 

340 

" 

50 

58.2 

93-7 

108.6 

163.3 

219.5 

272.4 

" 

IOO 
2OO 

45i.8 

84.9 
77-8 

98.4 
90.1 

I48.I 
135-7 

I98.I 
180.6 

245 
222.3 

<* 

400 

45-4 

72.1 

124.8 

1657 

203.1 

Barium  ferrocyanide 

0 

176 

277 

393 

521 

it                « 

2 

46.9 

75 

86.2 

I27-5 

166.2 

202.3 

ii                    a 

12.5 

30.4 

48.8 

56.5 

83-1 

107 

129.8 

Calcium  ferrocyanide 

O 

88 

146 

171 

271 

386 

512 

ii                ii 

2 

47.1 

75-5 

86.2 

130 

ii                ii 

I2-5 

31.2 

49-9 

57-4 

II                                    K 

5° 

24.1 

38-5 

44.4 

64.6 

81.9 

II                                    II 

IOO 

21.9 

35-i 

40.2 

58-4 

73-7 

84.3 

II                                    II 

2OO 

2O.6 

32-9 

37-8 

55 

6§.7 

77.5 

II                               K 

Potassium  citrate 

400 
0 

20.2 
76.4 

32.2 
124.6 

37-i 
144-5 

% 

67.5 
320 

76.2 

420 

ii              ii 

°*5 

— 

1  20.  1 

!39-4 

ii              «i 

2 

71 

1154 

J34-5 

2IO.I 

293-8 

381.2 

ii              i« 

5 

67.6 

109.9 

128.2 

198.7 

276.5 

357-2 

K                          « 

12.5 

62.9 

101.8 

118.7 

183.6 

254-2 

326 

" 

So 

54-4 

87.8 

102.  1 

157-5 

2I5-5 

273 

" 

IOO 

50.2 

80.8 

93-9 

143-7 

196.5 

247.5 

" 

300 

43-5 

69.8 

81 

I23-5 

167 

209.5 

Lanthanum  nitrate 

0 

122.7 

142.6 

223 

3J3 

534 

651 

ii               «< 

2 

68.9 

1  10.8 

128.9 

200.5 

279.8 

363-5 

4^7-5 

549  o 

"               " 

I2-5 

50 

61.4 

54 

98.5 
86.1 

114.4 
99-7 

176.7 
152-5 

243-4 
207.6 

311.2 
261.4 

3»3.4 
315-8 

447-8 
357-7 

«               K 

IOO 
200 

49.9 
46 

79-4 
72.1 

83*5 

139-5 
126.4 

189.1 
170.2 

236.7 

210.8 

282.5 
249.6 

316.3 
276.2 

From  the  investigations  of  Noyei  and  Johnston,  Journal  of  the  American  Chemical  Society,  31, 1909. 
SMITHSONIAN  TABLES. 


278  TABLES  284,  285. 

CONDUCTANCE  OF  IONS.  -  HYDROLYSIS  OF  AMMONIUM  ACETATE. 

TABLE  284.  -The  Equivalent  Conductance  of  the  Separate  Ions. 


Ion. 

0° 

18° 

25° 

So° 

75° 

100° 

128° 

I56° 

K  

4O  4 

646 

74.1 

II  Z 

I  CO 

206 

267 

Na    

26 

47.  C 

CO.Q 

82 

1oy 
116 

ICC 

*Hj 

2Q  7 

J1/ 

24Q 

NH4      

4.O.2 

64.  S 

74.  C 

lie 

i  t;o 

1  JJ 
2O  7 

^Uj 

264 

•JTQ 

As    , 

•12.0 

C4.-2 

63.5 

IOI 

14"? 

1  88 

2/1  c 

j^y 

2QQ 

ABa  

•jo 

552 

§ 

IO4 

I4Q 

^45 
262 

•*yy 

*Ca  

7O 

Si* 

68 

3 

142 

IQI 

2  C2 

j»* 

712 

{La       

7C 

61 

72 

IIQ 

177 

2-2  c 

•'O-6 
712 

788 

Cl     

41  I 

6c.c 

7  e  r 

116 

160 

•'Jj 
2O7 

J1-6 
2fiA 

7l8 

NO3  

40.4 

^i-o 
61.7 

7>5 
7O  6 

IO4 

I4O 

^u/ 
178 

222 

350 
267 

C2H8O2     .    . 
£S04     ... 
|C204    ... 
|C6H607    .    . 
jFe(CN)6.    .         . 

H      .... 

20.3 
41 

39 
36 

58 

240 

i 
34-6 
682 

632 
60 

95 

7,14 

40.8 

79 

73 
70 
in 

-ICQ 

67 
125 

"5 
"3 

i73 

/i6s 

14U 
96 

177 

^3 
161 

244 

c6c 

I30 

234 
2I3 
214 
32I 

644 

171 

303 

275 

722 

*WJ 
211 

370 
336 

777 

OH  

IOC 

172 

Oj" 

IQ2 

284 

i"i 
760 

C2  C 

CQ2 

JVAJ 

4JV 

J^J 

pl^ 

From  Johnson,  Journ.  Amer.  Chem.  Soc.,  31,  1909. 


TABLE  285.— Hydrolysis  of  Ammonium  Acetate  and  lonization  of  Water. 


Tempers  turc  . 

Percentage 
hydrolysis. 

lonization  constant 
of  water. 

Hydrogen-ion  concen- 
tration in  pure  water. 
Equivalents  per  litre. 

i 

XOOh 

KwXio" 

CHXio' 

o 

- 

0.089 

0.30 

18 

(0-35) 

0.46 

0.68 

25 

- 

0.82 

0.91 

too 

4.8 

48. 

6.9 

156 

18.6 

223. 

14.9 

218 

52-7 

46l. 

21.5 

306 

91.5 

1  68. 

13.0 

Noyes,  Kato,  Kanolt,  Sosman,  No.  63  Publ.  Carnegie  lust.,  Washington. 

SMITHSONIAN  TABLES. 


TABLES  286,  287.  279 

DIELECTRIC  CONSTANTS. 

TABLE  286. -Dielectric  Constant  (Specif io  Inductive  Capacity)  of  Gases. 
Atmospheric  Pressure. 

Wave-lengths  of  the  measuring  current  greater  than  10000  cm. 


Gas. 

Temp. 

°c: 

Dielectric  constant 
referred  to 

Authority. 

Vacuum=»i 

Air-i 

Air  

0 

20 

0 
100 

0 

o 

0 
0 

o 
o 

100 

0 
0 

o 

0 

0 
0 

0 
0 

145 

1.000590 
1.000586 

1.00718 

1.00290 
1.00239 

1.000946 
1.000985 

1.000690 
1.000695 

1.00131 
1.00146 

1.00258 

1.000264 
1.000264 

1.000944 
1.000953 

I.OOII6 
1.00099 

1.00093 
1.00905 

1.00705 

1.  000000 
1.  000000 

1.00659 

1.00231 
1.00180 

1.000356 
1.000399 

I.OOOIOO 

1.000109 

1.00072 
1.00087 

1.00199 

0.999674 
0.999678 

1.000354 
1.000367 

1.00057 

1.00041 

1.00934 

1.00846 
1.00646 

Boltzmann,  1875. 
Klemenclc',  1885. 

Badeker,  1901. 

KlemenclC. 
Badeker. 

Boltzmann. 
KlemenCiC. 

Boltzmann. 
KlemenclC. 

Boltzmann. 
KlemenCiC. 

Badeker. 

Boltzmann. 
KlemenclC. 

Boltzmann. 
KlemenCiC. 

Boltzmann. 
Klemenclc". 

Badeker. 
KlemenCiC. 

Badeker. 

« 

Carbon  bisulphide     .    .    . 

Carbon  dioxide      .... 
it            « 

Carbon  monoxide  .... 
«              «« 

Ethylene  

M 

Hydrochloric  acid      .    .    . 

M 

Nitrous  oxide  (N2O)      .    . 

(4                    «<                    <« 

Sulphur  dioxide    .... 
«<            « 

Water  vapor,  4  atmospheres 

TABLE  287. -Variation  of  the  Dielectric  Constant  with  the  Temperature. 

For  variation  with  the  pressure  see  next  table. 

If  £>e  =  the  dielectric  constant  at  the  temperature  8°  C.,  Dt  at  the  tempera- 
ture /°  C.,  and  a  and  &  are  quantities  given  in  the  following  table,  then 

&9  =  Dt  [i  —  «(/— 6)  +  $(t— 6)2]. 
The  temperature  coefficients  are  due  to  Badeker. 


Gas. 

a 

ft 

Range  of 
temp.  °  C. 

Ammonia     .    . 

5.45  X  IO-* 

2.59  X  icr7 

10  —  110 

Sulphur  dioxide 

6.I9XIQ-6 

1.86  X  icr7 

0  —  110 

Water  vapor     . 

1.4X10-* 

- 

145 

The  dielectric  constant  of  air  at  atmospheric  pressure  but  with  varying  tem- 
perature may  also  be  calculated  from  the  tact  that  D  —  i  is  approximately  pro- 
portional  to  the  density. 
SMITHSONIAN  TABLES. 


280  TABLES  288,  289, 

DIELECTRIC  CONSTANTS  (continued). 
TABLE  288.  -Change  of  the  Dielectric  Constant  of  Gases  with  the  Pressure. 


Gas. 

Temper- 
ature/* C. 

Pressure 
atmos. 

Dielectric 
constant. 

Authority. 

Air            .... 

IQ 

2O 

I  0108 

Tan?!   IQO7 

4.O 

I.  O2l8 

60 

j  O7"?O 

«          « 

80 

I  O4.7Q 

«          « 

IOO 

I«u4jy 
i  ocd.8 

«          « 

II 

20 

I.OIOI 

Occhialini  1905 

4.O 

I  0196 

60 

I  O2QJ. 

(( 

80 

I.O^S? 

u 

IOO 

I  0482 

a 

1  20 

I.OC7Q 

« 

IAQ 

IO67A 

« 

140 

160 

I  0760 

«                 « 

1  80 

I  O84"; 

«                 « 

Carbon  dioxide  .    . 
«            « 

«            « 

Nitrous  oxide,  NgO 
«           ««         «« 

«           <«         <« 

15 
15 

10 
20 
40 
IO 
20 
40 

1.008 
1.020 
1.  060 
I.OIO 

1.025 
1.070 

Linde,  1895. 
<«        « 

«        <« 
« 
«« 
« 

TABLE  289.  -Dielectric  Constants  of  Liquids. 
A  wave-length  greater  than  10000  centimetres  is  denoted  by  oo , 


Substance. 

Temp. 

°c: 

Wave- 
length, 
cm. 

Dielectric 
constant. 

|. 

1* 

Substance. 

Temp. 

°c: 

Wave- 
length, 
cm. 

Dielectric 

constant* 

1* 

Alcohol: 

Alcohol  : 

Amyl 

frozen 

00 

2.4 

Methyl     . 

-50 

00 

45-3 

u 

—  IOO 

«« 

30.1 

« 

0 

« 

35-° 

« 

—50 

«« 

23.0 

M 

+20 

« 

31.2 

« 
« 

o 

+  20 

M 

H 

17.4 

1  6.0 

« 

Propyl      . 

17 
—  120 

75 

00 

33-2 
46.2 

" 

18 

200 

10.8 

«« 

—60 

(( 

33-7 

«< 

18 

73 

4-7 

M 

0 

• 

24.8 

Ethyl 

frozen 

00 

2.7 

U 

+  20 

" 

22.2 

«i 

—  120 

<( 

54-6 

« 

IS 

75 

12.7 

2 

N 

-80 

H 

44-3 

Acetone  .     . 

—80 

00 

33-8 

5 

« 

H 
« 

—40 
0 
+20 

<« 
H 
(I 

i 

«« 
<« 

O 
15 
17 

I2OO 

73 

26.6 
21.85 
20.7 

i 

« 

17 

2OO 

24.4 

2 

Acetic  acid 

18 

00 

9-7 

8 

«l 

« 

75 

23.0 

2 

«             u 

15 

1  200 

10.3 

6 

M 

H 

53 

20.6 

3 

<!                <« 

17 

200 

7.07 

2 

«l 

(4 

4 

8.8 

3 

«                (« 

19 

75 

6.29 

2 

rt 

« 

0.4 

5-o 

4 

Amyl  acetate 

19 

00 

4.81 

9 

Methyl 
« 

frozen 
—  IOO 

00 
« 

58.0 

i 

Amylene 

16 

«« 

2.2O 

10 

References  on  page  281. 


SMITHSONIAN  TABLES. 


TABLE  289  (continued). 
DIELECTRIC  CONSTANTS  OF  LIQUIDS. 

A  wave-length  greater  than  10000  centimetres  is  designated  by  oo . 


281 


Substance. 

Temp. 

Wave- 
length 
cm. 

Diel. 
const. 

jj 

g.tJ 

Substance. 

Temp. 

Wave- 
length 
cm. 

Diel. 
const. 

j* 

(frozen) 

Anilin       .... 

18 

oo 

7  lift 

J  i 

Nitrobenzol  ... 

—  IO 

oo 

0.0 

j 

Benzol  (benzene)  . 

18 

2^288 

U 

—5 

M 

s  s 

42.0 

" 

«              « 

19 

73 

2.26 

2 

"           ... 

o 

it 

41.0 

" 

Bromine  .... 

23 

84 

3.18 

12 

"           ... 

H~ZS 

" 

37-8 

" 

Carbon  bisulphide 

20 

00 

2.626 

13 

M 

30 

" 

" 

«<                u 

17 

73 

2.64 

2 

4( 

18 

" 

36-45 

II 

Chloroform  .    .    . 

18 

00 

5-2 

II 

"                      ... 

17 

73 

34-0 

2 

M 

17 

73 

4-95 

2 

Octane     .... 

17 

00 

1.949 

16 

Decane    .... 

14 

00 

1.97 

10 

Oils: 

Decylene      .    .    . 

« 

2.24 

« 

Almond     .    .    . 

20 

00 

2.83 

18 

Ethyl  ether       .    . 

—  80 

00 

7-05 

5 

Castor  .... 

II 

* 

4.67 

19 

"        "      •    • 

—40 

5-67 

« 

Colza    .... 

20 

'* 

3-11 

20 

"        "... 

o 

4.68 

M 

Cottonseed    .    . 

14 

« 

3.10 

21 

«               "... 

18 

4-368 

II 

Lemon  .... 

21 

«« 

2.25 

22 

"              "... 

20 
60 

4-30 
3-65 

13 

Linseed     .    .    . 
Neatsf  oot  .    .    . 

13 

«, 

3-35 
3.02 

21 
20 

«               "... 

IOO 

3.12 

« 

Olive     .... 

20 

" 

3-11 

23 

"               "... 

140 

2.66 

« 

Peanut.     .    .    . 

II.4 

« 

3-°3 

21 

"              "... 

180 

2.12 

« 

Petroleum     .     . 

2OOO 

2-13 

24 

Crit. 

Petroleum  ether 

20 

00 

1.92 

20 

41                (1 

temp. 

44 

Rape  seed     .    . 

16 

0 

2.85 

21 

Formic  acid      .    . 
Glycerine     .    .    . 

M 

192 

18 

+2 
(frozen) 

II 

15 
1C 

83 

73 
1  200 
73 

1200 
20O 

'•53 

4-35 
19.0 

62.0 
58.5 
56.2 

14 

2 

6 

2 

6 

2 

Sesame     .    .    . 
Sperm  .... 
Turpentine    .     . 
Vaseline   .    .    . 
Phenol      .... 
Toluol      .... 

13-4 

20 
20 

4*8 
-83 

+16 

73 

00 

3.02 

2.23 
2.17 
9.68 
2.51 
2-33 

2O 

25 
2 

5 

« 

J 

H 

25-4 

f< 

19 

73 

00 

2-3I6 
2.376 

2 
II 

Meta-xylol    .     .     . 

N 

_ 

"•  J 

0.4 

2^6 

4 

.    .    . 

17 

73 

2-37 

2 

PTexane 

T*7 

T  R5?rt 

Tfi 

Hydrogen  perox-  ) 
ide46%inH2O  J 

18 

OO 

75 

84.7 

1U 

17 

Water      .... 
for  temp,  coeff. 

18 
17 

00 
2OO 

81.07 
80.6 

II 

2 

see  Table. 

17 

74 

8l.7 

M 

17 

38 

83.6 

II 

i  Abegg-Seitz,  1899.             10  Landolt-Jahn,  1892.                  18  Hasenohrl,  1896. 

2  Drude,  1896.                       n  Turner,  1900.                            19  Arons-Rubens,  1892. 

3  Marx,  1898.                         12  Schlundt.                                   20  Hopkinson,  1881. 

4  Lampa,  1896.                      13  Tangl,  1903.                              21  Salvioni,  1888. 
5  Abegg,  1897.       .                14  Coolidge,  1899.                         22  Tomaszewski,  1888. 
6  Thwing,  1894.                     15  v.  Lang,  1896.                           23  Heinke,  1896. 
7  Drude,  1898.                       16  Nernst,  1894.                            24  Marx. 

8  Francke,  1893.                   17  Calvert,  1900.                          25  Fuchs. 

9  Lowe,  1898. 

SMITHSONIAN  TABLES. 


282 


TABLES  290-291. 

DIELECTRIC  CONSTANTS  OF  LIQUIDS  (continual). 
TABLE  290.— Temperature  Coefficients  of  the  Formula : 


Substance. 

a 

0 

Temp, 
range,  6  C. 

Authority. 

Amyl  acetate  .    .     . 

0.0024 

O  OO"KI 

- 

- 

Lowe. 
Ratz 

O  OOIO6 

00000087 

IO-4.O 

Hasenohrl 

Carbon  bisulphide  . 

Chloroform    .    .    . 
Ethyl  ether     .    .    . 
Methyl  alcohol    .     . 
Oils:  Almond    .     . 
Castor  .     .    . 
Olive    .    .    . 
Paraffine  .    . 

Toluol   
«« 

0.000966 
0.000922 
0.00410 
0.00459 

0.0057 

0.00163 
0.01067 

0.00364 
0.000738 
0.000921 

O.OOOQ77 

0.00000060 
0.000015 

0.000026 

0.0000072 
0.00000046 

20-181 

22-1  8  I 
O-I3 

20-181 

Ratz. 
Tangl. 

M 

Ratz. 
Drude. 
Hasenohrl. 
Heinke,  1896. 

«                     44 

Hasenohrl. 
Ratz. 
Tangl. 

Water    .... 

O.OO4474. 

C—  2O 

Heerwagen 

«i 
44 

0.004583 
O.OO4l6 

O.OOOOII7 

•)     ^U 

0-76 

4-25 

Drude. 
Coolidge. 

Meta-xylol      .    .    . 

0.000817 

— 

20-181 

Tangl. 

(See  Table  287  for  the  signification  of  the  letters.) 


TABLE  291. -Dielectric  Constants  of  Liquified  Oases. 
A  wave-length  greater  than  loooo  centimetres  is  designated  by  oo. 


Substance. 

Temp. 

»' 
i 

Dial. 

constant. 

o 

3 

Substance. 

Temp. 
°C 

|| 

Dial, 
constant. 

} 

Air    

—191 

00 

1.432 

I 

Nitrous  oxide 

H 

4( 

7  C 

1.47—  i.  so 

2 

N2O 

—88 

00 

I.OTg 

s 

Ammonia  .    .    . 

—34 

7.S 

21-23 

3 

44                       44 

—5 

H 

1.630 

5 

"     .... 

no 

16.2 

4 

~t~5 

1.57s 

Carbon  dioxide  . 

—5 

oo 

i.6og 

s 

44                    44 

+  J5 

44 

1.520 

«4 

44                       44 

o 

44 

1.583 

44 

Oxygen      .    .    . 

—182 

44 

1.491 

9 

44                       44 

-fio 

44 

i-54o 

44 

44 

4<       . 

44 

1.465 

8 

44                       44 

-MS 

44 

1-526 

(4 

Sulphur  dioxide  . 

14-5 

120 

13.75 

4 

Chlorine    .    .    . 

—60 

44 

2.150 

44 

44                            44 

20 

CO 

14.0 

6 

44 

—  20 

44 

2.030 

4« 

44                          44 

40 

" 

12.3 

44 

0 

44 

1.970 

60 

10.8 

44 

+10 

44 

i-94o 

44 

44                          44 

80 

44 

9.2 

44 

44 

O 

44 

2.08 

6 

44                          44 

IOO 

7.8 

44 

+14 

100 

1.88 

4 

44                          44 

120 

44 

6.4 

44 

Cyanogen  .    .    . 
Hydrocyanic  acid 
Hydrogen  sulph. 

23 

21 
10 

84 

44 

OO 

2.52 
about  95 

5-93 

44 

6 

44                        II 

Critical.    .    .    ! 

140 
154.2 

(4 

44 

4.8 

2.1 

44 
44 

50 

4.92 

44                         44 

9° 

44 

376 

44 

I  v.  Pirani,  1903.                              4  Coolidge,  1899.               7  Schlundt,  1901. 
2  Bahn-Kiebitz,  1904.                        5  Linde,  1895.                     8  Hasenohrl,  1900. 
3  Goodwin-Thompson,  1899.           6  Eversheim,  1904.'           9  Fleming-Dewar,  1896. 

SMITHSONIAN  TABLES. 


TABLES  292,  293.-DIELECTRIC  CONSTANTS  (continued).  283 

TABLE  292.  —  Standard  Solutions  for  the  Calibration  o!  Apparatus  for  the  Measuring  of  Dielectric  Constants. 


Turner. 

Drude. 

Nernst. 

Substance. 

Diel.  const, 
at  18°. 

\==  CO. 

Acetone  in  benzol  at  19°.    A  =  75  cm. 

Ethyl  alcohol  in 
water  at  19.5°. 
A=  oo. 

Per  cent 

by  weight. 

Density  16°. 

Dielectric 
constant. 

Temp, 
coefficient. 

2.288 
2.376 

4.36; 

7.298 

10.90 

27.71 
36.45 

81.07 

Per  cent 
by  weight. 

Dielectric 
constant. 

Meta-xylol    .... 
Ethyl  ether   .... 

O 
2O 

40 
60 
80 

IOO 

0.885 
0.866 
0.847 
0.830 
0.813 
0.797 

2.26 

CIO 

8.43 
I2.I 
1  6.2 

20.5 

0.1% 

o-3 
0.4 

o-5 
o-5 
0.6 

IOO 
90 
§0 

70 
60 

26.0 
29-3 

£! 

43-i 

Ethyl  chloride  .    .    . 
O-nitro  toluol    .    .    . 
Nitrobenzol  .... 
Water  (conduct.  IO"6) 

Water  in  acetone  at  19°.    A  =  75  cm. 

0 
20 
40 
60 
80 
IOO 

0.797 
0.856 
0.903 
0.940 

0.973 
0-999 

20.5 
31-5 

43-5 

Li 

0.6% 
0-5 
o-5 
o-S 

0. 

0.4 

TABLE  293. -Dielectric  Constants  of  Solids. 


Substance. 

Condi- 
tion. 

Wave- 

length, 
cm. 

Dielectric 
constant. 

Jk 

1" 

Substance. 

Condi- 
tion. 

Wave- 
length, 
cm. 

Dielectric 
constant. 

1* 

Asphalt      .     . 

_ 

00 

2.68 

i 

Temp. 

Barium      sul- 

Iodine (cryst.)  . 

23 

75 

4.00 

2 

phate      .    . 

_ 

75 

10.2 

2 

Lead  chloride  . 

Caoutchouc   . 

_ 

00 

2.22 

3 

(powder) 

_ 

M 

42 

2 

Diamond   .    . 

_ 

« 

I6.S 

"     nitrate      . 

_ 

« 

16 

2. 

« 

_ 

75 

5-5° 

2 

"     sulphate  . 

— 

« 

28 

2 

Ebonite     .    . 

- 

00 

2.72 

4 

"     molybde- 

M 

— 

« 

2.86 

5 

nate  .    . 

_ 

«« 

24 

2 

M 

_ 

1000 

2-55 

6 

Marble 

Glass* 

Density. 

(Carrara) 

_ 

M 

8-3 

2 

Flint  (extra 

Mica   .... 

_ 

OO 

5.66-5.97 

5 

heavy) 
Flint    (very 

4-5 

00 

9.90 

7 

Madras,  brown 

- 

« 
« 

5.80-6.62 
2.5-34 

II 

light)  .     . 

2.87 

(1 

6.61 

7 

"        green 

_ 

« 

3-9-5-5 

16 

Hard  crown 

2.48 

« 

6.96 

7 

"        ruby  . 

_ 

« 

4.4 

16 

Mirror    .    . 

« 

6.44-7-46 

5 

Bengal,  yellow 

- 

If 

2.8 

16 

« 
Lead  (Pow- 

- 

M 

600 

5-37-5-90 
5.42-6.20 

8 
8 

"      white  . 
"      ruby    . 
Canadian    am- 

-    • 

« 

« 

4.2 
4.2-4.7 

16 
16 

ell).     .    . 

3-0-3-5 

00 

5.4-8.0 

9 

ber  .     .    .    . 

_ 

« 

3-o 

16 

Jena 

South  America 

_ 

« 

5-9 

16 

Boron      . 
Barium    . 

: 

« 
« 

5.3-8.1 

7.8-8.5 

10 

TO 

Ozokerite  (raw) 
Paper        (tele- 

— 

M 

2.21 

i 

Borosili- 

phone) 

_ 

<{ 

2.0 

17 

cate 

_ 

« 

6.4-7.7 

i 

"      (cable) 

_ 

M 

2.0-2.5 

i 

Gutta  percha  . 

- 

- 

3-3-4-9 

ii 

Paraffine 

Melting 

<« 

2.46 

18 

Temp. 

«< 

point. 

<« 

2.32 

19 

Ice    .... 

—  $ 

1200 

.     2.85 

12 

« 

44-46 

« 

2.IO 

20 

«  ;  ;  .*  ; 

—18 

—190 

5OOO 

75 

3-i6 
1.76-1.88 

13 
14 

« 

M 

54-56 
74-76 

«« 
« 

2.14 
2.16 

20 

20 

References  on  p.  284. 

*  For  the  effect  of  temperature,  see  Gray-Dobbie,  Pr.  Roy.  Soc.  63,  1898;  67,  1900. 
"  wave-length,  see  K.  F.  Lowe,  Wied.  Ann.  66,  1898. 

SMITHSONIAN  TABLES. 


284 


TABLES  293,  294. 

DIELECTRIC  CONSTANTS  (continued). 
TABLE  293.  — Dielectric  Constant!  of  Solids  (continued). 


Substance. 

Condi- 
tion. 

Wave- 
length, 
cm. 

Diel. 
constant. 

1  Author-)  1 
|  ity.  1 

Substance. 

Condi- 
tion. 

Wave- 
length, 
cm. 

Diel. 
constant. 

I.S 


Paraffine    .    . 

47-°6 

61 

2.16 

21 

Sulphur 

"          .    . 

56.°2 

61 

2.25 

21 

Amorphous 

- 

00 

3-98 

i 

Phosphorus  : 

" 

_ 

75 

3.80 

2 

Yellow    .    . 

- 

75 

3-60 

2 

Cast,  fresh 

- 

00 

4.22 

I 

Solid  .    .    . 

— 

80 

4.1 

22 

u        u 

— 

u 

4-05 

18 

Liquid     .     . 

— 

80 

3-85 

22 

ii        ii 

_ 

75 

3-95 

2 

Porcelain: 

Cast,  old    . 

_ 

oo 

3.60 

18 

Hard 

u        u 

_ 

75 

3-9° 

2 

(Royal  B'l'n) 

- 

00 

5-73 

15 

( 

near 

Seger   "  "     . 

- 

II 

6.61 

15 

Liquid     .  < 

melting- 

i  °° 

3-42 

I 

Figure"  "     . 

— 

II 

6.84 

15 

I 

point 

) 

Selenium  .     . 

- 

II 

7-44 

I 

Strontium 

"           .    . 

- 

75 

6.60 

2 

sulphate 

- 

75 

"•3 

2 

" 

— 

00 

6.13 

23 

Thallium 

"           .     . 

- 

IOOO 

6.14 

23 

carbonate 

- 

75 

17 

2 

[Shellac.    .    . 

— 

00 

3.10 

4 

"  nitrate     . 

_ 

75 

16.5 

2 

"      ... 

_ 

" 

2-95-3-73 

24 

Wood 

dried 

.    .    . 

— 

II 

25 

Red  beech  . 

||  fibres 
-I-    " 

00 

4.83-2.51 

- 

Oak  .     .     ! 

II     " 

II 

4.22-2.46 

_ 

"      ... 

_L    " 

II 

6.84-3.64 

— 

i  v.  Pirani,  1903.                         10  Lowe,  1898.                              18  Fallinger,  1902. 

2  Schmidt,  1903.                         n  (submarine-data).                     19  Boltzmann,  1875. 

3  Gordon,  1879.                          I2  Thwing,  1894.                          20  Zietkowski,  1900. 

4  Winklemann,  1889.                 13  Abegg,  1897.                            21  Hormell,  1902. 
5  Elsas,  1891.                              14  Behn-Kiebitz,  1904.                 22  Schlundt,  1904. 

6  Ferry,  1897.                               15  Starke,  1897.                             23  Vonwiller-Mason,  1907. 
7  Hopkinson,  1891.                    16  E.  Wilson.                                24  Wiillner,  1887. 

8  Arons-Rubens,  1891.              17  Campbell,  1906.                       25  Donle. 

9  Gray-Dobbie,  1898. 

TABLE  294.— Dielectric  Constants  of  Crystals. 
Do,  D/8,  D7  are  the  dielectric  constants  along  the  brachy,  macro  and  vertical  axes  respectively. 


Substance. 

Wave- 
length, 
cm. 

Diel.  const. 

i 

o 

•£  * 
ts-  s 
< 

Substance. 

Wave- 
length, 
cm. 

Diel.  const. 

Author-  1 

j_  Axis. 

I  Axis. 

Da 

D/3 

Dy 

UNIAXIAL  : 
Apatite    .... 
Beryl   .... 

75 

00 

ii 
75 

00 
II 

75 
75 

00 
II 

IOOO 

75 
75 

00 

75 

75 

9-50 
7-85 
7.10 
6.05 
8.49 
8.78 

B 

4.69 

4.27 

4-32 
89 

7-i3 
6-75 

12.8 

7.40 

7-44 
6.05 

5-52 
7.56 
8.29 
6.80 

8.00 
5.06 
4.46 

4-34 
4.60 

173 
6.54 
5.65 

12.6 

i 
2 

3 

4 

5 
i 

i 

4 
6 
6 

i 
i 

4 
i 
i 

RHOMBIC  : 

Arragonite   .    .     . 

<i 

Barite  .     .              . 

oo 

75 
oo 

75 
75 
75 

00 
M 
« 
II 
II 

75 
75 

9.14 
9.80 
6.97 

7.65 
7.70 

25-4 
|.26 
6.09 
6.70 
3.8l 

3-65 
3.62 
6.65 

7.68 
10.09 

12.20 
I8.5 
23.2 
6.05 

Sr 

6.92 

3-97 
3-85 
3-85 
6.70 

7-13 
6-55 
7.00 
7.70 
8.30 
19.2 
8.28 

4-77 
4.66 
4.66 
6.30 

4 

4 
i 

i 

7 
7 

I 

7 
i 

I 

ii 

ii 

« 

Calcspar  .    .    . 

Dolomite  .     .    . 
Iceland  spar 

Quartz     .     .     . 
i< 

Ccelestin  .... 
Cerussite      .    .     . 
MgS04  +  7H20  . 
K2S04     .... 
Rochelle  salt     .     . 
Sulphur   .... 
« 

ii 

it 

ii 

Rutil(Ti02).    .    . 
Tourmaline  .     .     . 

Topaz  . 

i  Schmidt,  1903.                       4  Fallinger,  1902.                     7  Borel,  1893. 
2  Starke,  1897.                          5  v.  Pirani,  1903.                     8  Boltzmann,  1875. 
3  Curie,  1889.                            6  Ferry,  1897. 

SMITHSONIAN  TABLES. 


TABLE  295. 


285 


VARIATION    OF   ELECTRICAL    RESISTANCE   OF  CLASS  AND   PORCELAIN 

WITH   TEMPERATURE. 

The  following  table  gives  the  values  of  a,  6,  and  c  in  the  equation 

log  R  =  a  +  bt  +  cfl, 

where  R  is  the  specific  resistance  expressed  in  ohms,  that  is,  the  resistance  in  ohms  per  centimetre  of  a  rod  ono 
square  centimetre  in  cross  section.* 


Range  of 

No. 

Kind  of  glass. 

Density. 

a 

6 

C 

temp. 

Centigrade. 

I 

Test-tube  glass          .... 

- 

13-86 

—.044 

.000065 

0°-250° 

2 

«      <«        « 

2.41:8 

14.24 

—  .occ 

.0001 

•57—1  -ii 

1  6.21 

—  .047 

.OOOO  104. 

6o-I74 

4 

Lime  glass  (Japanese  manufacture)  . 

2-55 

I3-H 

—.031 

—  .000021 

10-85 

5 

«         «            «                   « 

2.499 

14.002 

—  .025 

—  .00006 

35-95 

6 

Soda-lime  glass  (French  flask) 

2-533 

14.58 

—.049 

.000075 

45-120 

7 

Potash-soda  lime  glass      .        . 

2.58 

16.34 

—.0425 

.0000364 

66-193 

8 

Arsenic  enamel  flint  glass         . 

3-07 

18.17 

—•055 

.000088 

io5-!35 

9 

Flint  glass  (Thomson's  electrometer 

jar)        

3>!72 

18.021 

—.036 

—  .0000091 

i  00-200 

10 

Porcelain  (white  evaporating  dish)  . 

- 

15-65 

—  .042 

.00005 

68-290 

COMPOSITION  OF  SOMB  OF  THE  ABOVE  SPECIMENS  OF  GLASS. 

Number  of  specimen  = 

3 

4 

6 

7 

8 

9 

Silica      

61.3 

57-2 

70.05 

75.65 

54-2 

55-18 

Potash    

22.Q 

21.  1 

1.44 

7.  Q2 

IO.C 

17.28 

Soda       

Lime,  etc. 

Lime,  etc. 

1  4.  -32 

6.Q2 

7.O 

Lead  oxide     .... 

bydiff. 

bydiff. 

2.70 

23.9 

31.01 

Lime      

15.8 

16.7 

10-33 

8.48 

o-3 

0-35 

Magnesia        .... 

- 

- 

- 

0.36 

0.2 

O.o6 

Arsenic  oxide 

- 

- 

- 

•      - 

3-5 

- 

Alumina,  iron  oxide,  etc. 

- 

- 

145 

0.70 

0.4 

0.67 

SMITHSONIAN  TABLES. 


*  T.  Gray,  "Phil.  Mag."  1880,  and " Proc.  Roy.  Soc."  i88a. 


286 


TABLES  296,  297. 
PERMEABILITY  OF  IRON. 

TABLE  296.— Permeability  of  Iron  Rings  and  Wire. 


This  table  gives,  for  a  few  specimens  of  iron,  the  magnetic  induction  B,  and  permeability  /*,  corresponding  to  th« 
magneto-motive  forces  H  recorded  in  the  first  column.  The  first  specimen  is  taken  from  a  paper  by  Rowland,* 
and  refers  to  a  welded  and  annealed  ring  of  "Burden's  Best "  wrought  iron.  The  ring  was  6.77  cms.  in  mean 
diameter,  and  the  bar  had  a  cross  sectional  area  of  0.916  sq.  cms.  Specimens  2-4  are  taken  from  a  paper  by 
Bosanquet,t  and  also  refers  to  soft  iron  rings.  The  mean  diameters  were  21.5,  22.1,  and  22.725  cms.,  and  the 
thickness  of  the  bars  2.535,  1.295,  an^  -7544  cms.  respectively.  These  experiments  were  intended  to  illustrate  the 
effect  of  thickness  of  bar  on  the  induction.  Specimen  5  is  from  Ewing's  book,$  and  refers  to  one  of  his  own 
experiments  on  a  soft  iron  wire  .077  cms.  diameter  and  30.5  cms.  long. 


Specimen  1 

2 

3 

4 

6 

ft*it 

H 

B 

M 

B 

ft. 

B 

B 

B 

silis 

£*  !•!  I 

ifitH 

0.2 

80 

33° 

400 
660 

126 

377 

630 

754 

65 

224 

323 
448 

85 
214 

Si 

22 

74 

no 

148 

ifl'g.s 

I.O 

145° 

145° 

1449 

1449 

840 

840 

88s 

885 

246 

246 

2.0 

4840 

2420 

4564 

2282 

3533 

1766 

2417 

1208 

950 

475 

H  «  i  §  8 

5-° 

9880 

1976 

9900 

1980 

8293 

1659 

8884 

1777 

12430 

2486 

|  -5  ^  %£ 

IO.O 

12970 

1297 

13023 

1302 

12540 

1254 

11388 

H39 

15020 

1502 

M«g  ^  j~   C 

2O.O 
50.0 

14740 
16390 

737 
328 

14911 
16217 

746 
324 

14710 
16062 

735 
321 

13273 
13890 

664 

278 

15790 

789 

%1 

1  00.0 

17148 

171 

17900 

179 

H837 

148 

>  o1?  ? 

TABLE  297. -Permeability  of  Transformer  Iron.§ 

This  table  contains  the  results  of  some  experiments  on  transformers  of  the  Westinghpuse  and  Thomson-Houston 
types.  Referring  to  the  headings  of  the  different  columns,  Mis  the  total  magneto-motive  force  applied  to  the  iron ; 
M '/ 1  the  magneto-motive  force  per  centimetre  length  of  the  iron  circuit ;  B  the  total  induction  through  the  mag- 
netizing coil ;  B  /  a  the  induction  per  square  centimetre  of  the  mean  section  of  the  iron  core  ;  M / B  the  magnetic 
reluctance  of  the  iron  circuit;  Bl/Ma  the  permeability  of  the  iron,  a  being  taken  as  the  mean  cross  section  of  the 
iron  circuit  as  it  exists  in  the  transformer,  which  is  thus  slightly  greater  than  the  actual  cross  section  of  the  iron. 


(a)  WESTINGHOUSK  No.  8  TRANSFORMERS  (ABOUT  2500  WATTS  CAPACITY).            r 

First  specimen. 

Second  specimen. 

M 

~T 

B 

il 

Bl 

B 

M 

Bl 

B 

a 

B 

Ma 

B 

a 

~B 

Ma 

20 

0-597 

2i8Xio8 

1406 

0.917  X  lo-4 

2360 

16  X  io4 

1032 

1.25  Xio-4 

1730 

40 

1.194 

387    " 

•    3790 

0.681         " 

3120 

49      « 

3140 

0.82        " 

2640 

00 

1.791 

878    " 

5660 

0.683        " 

3180 

82      « 

5290 

0.73        « 

2970 

80 

2-338 

1091      " 

7040 

0-734 

2960 

104      « 

6710 

0.77      " 

2820 

IOO 

2.985 

1219    " 

7860 

0.819 

2640 

118      « 

7610 

0.85      " 

2560 

120 

3-582 

1330    « 

8580 

0.903 

2410 

124      " 

8000 

o-97      " 

2250 

I4O 

160 

4.179 
4.776 

1405    « 
1475    " 

9060 
9510 

0.994 

2186 
2OOO 

131       « 
135      " 

8450 
8710 

1.07      " 
1.18      " 

2036 
1830 

1  80 

5-373 

1532    " 

9880 

1.180 

1850 

140      " 

9030 

1.29      " 

1690 

200 

5-970 

1581        " 

10200 

1.270 

1720 

142      « 

9160 

1.41      w 

1540 

220 

6.567 

1618      " 

10430 

1.360 

!59° 

144 

9290 

1-53      " 

1410 

260 

7.761 

1692      " 

I09IO 

1.540 

1410 

SMITHSONIAN  TABLES. 


*  "  Phil.  Mag."  4th  series,  vol.  xlv.  p.  151. 

t  Ibid,  sth  series,  vol.  xix.  p.  73. 

J  "  Magnetic  Induction  in  Iron  and  Other  Metals," 

§  T.  Gray,  from  special  experiments. 


TABLE  297  (continued). 
PERMEABILITY    OF   TRANSFORMER    IRON. 


28; 


(to)  WESTINGHOUSE  No.  6  TRANSFORMERS  (ABOUT  1800  WATTS  CAPACITY). 

First  specimen. 

Second  specimen. 

M 

T 

B        M 

Bl 

B 

M 

Bl 

B 

a        B 

Ma 

B 

a 

B 

Ma 

20 

0.62 

I47XI08 

1320   I.36XIO-4 

2140 

2I5XI08 

1940 

0.93X10-4 

3HO 

40 
60 

1.23 

1.85 

442  " 
697  « 

3980   0.91   " 

6280  0.86  " 

3260 

339° 

615 
826 

5540 
7440 

0.64   " 
0.72   « 

4490 
4030 

80 

2.46 

862  " 

7770   0.93  " 

986 

8880 

0.81  « 

3590 

IOO 

3.08. 

949  « 

8550   1.05  ' 

2770 

1050 

9460 

0.95  " 

3060 

120 

3-70 

1010  " 

9106    .19  ' 

2450 

I  IOO 

9910 

1.09  « 

2670 

140 

160 

4-31 
4-93 

1060  « 
1090  " 

955°   -33  " 
9820   .47  " 

22IO 
1990 

II4O 
1170  " 

10300 
10500 

1.23  " 
1.37  « 

2430 
2180 

180 

5-55 

1  120  " 

IOIOO    .6l   " 

1830 

1190  " 

10700 

i-5i 

1970 

200 

6.16 

1150  " 

10400   .74  " 

I680 

" 

(0)  WESTINGHOUSE  No.  4  TRANSFORMER 
(ABOUT  1200  WATTS  CAPACITY). 

(d)  THOMSON-HOUSTON  1500  WATTS  TRANSFORMER. 

M 

B 

M 

Bl 

M 

B 

M 

Bl 

M 

T 

B 

a 

B 

Ma 

M 

~l 

B 

a 

B 

Ma 

2O 

0.69 

i47Xio3 

1470 

I.36XIO-4 

2140 

20 

0.42 

70XI08 

1560 

2.86X10-4 

3730 

40 

0.84 

142  " 

3160 

2.81  " 

3780 

40 

1.38 

406  " 

4066 

0.98   " 

2940 

60 

1.26 

214  ' 

4770 

2.8  1   " 

379° 

80 

1.68 

265  < 

59!0 

3.02  « 

3520 

DO 

2.07 

573  " 

S73° 

I.OS   « 

2770 

IOO 

2.10 

309  • 

6890 

3-24  ' 

3280 

80 

2.76 

659  " 

6590 

I.2I   " 

2390 

120 

160 

2.52 
3.36 

348  ' 
408  ' 

7760 
9100 

345  " 
3.92  « 

3080 
2710 

200 

4-2O 

456  ' 

IO2OO 

4-39  " 

2430 

IOO 

345 

714  « 

7140 

1.40   " 

2070 

240 

5-°4 

495  ' 

IIOOO 

4.87  « 

2190 

1  20 

4.14 

748  « 

7490 

1.  60   " 

1810 

280 
320 

5.88 
6.72 

524  " 
550  '< 

11690 

12270 

1990 
1820 

140 

4-83 

777  " 

7770 

1.  80   " 

1610 

360 
400 

7-56 
8.40 

573  ;; 
591  " 

12780 
13180 

6.29  « 
6.78  " 

1690 
1570 

440 

9.24 

504  " 

7.28  « 

1460 

288  TABLES  298-300.    MAGNETIC  PROPERTIES  OF  IRON. 

TABLE  298.  — Magnetic  Properties  of  Iron  and  Steel. 


Electro- 
lytic 
Iron. 

Good 
Cast 
Steel. 

Poor 
Cast 
Steel. 

Steel. 

Cast 
Iron. 

Electrical  Sheets. 

Ordinary. 

Silicon 
Steel. 

c 

Si 
Chemical  composi-    Mn 

tion  in  per  cent       p 
S 

0.024 
0.004 
0.008 
0.008 
O.OOI 

0.044 
0.004 
0.40 
0.044 
0.027 

0.56 
0.18 
0.29 
0.076 
0-035 

0.99 
O.IO 

0.40 
0.04 
0.07 

3-i  i 
3-27 
0.56 
1.05 
0.06 

0.036 
0-330 
0.260 
0.040 
0.068 

0.036 
3-90 
0.090 
0.009 
0.006 

Coercive  force    .    .    .   • 

2.83 
[0.36] 

[0-37] 

7-i 

(44-3) 

16.7 
(52.4) 

11.4 
[4-6] 

[1-30] 

[0-77] 

Residual  B     .    .    .    .    | 

11400 
[10800] 

10600 
[nooo] 

10500 
(10500) 

13000 
(7500) 

5100 
[5350] 

[9400] 

[9850] 

Maximum  permeability  < 

1850 
[14400] 

355° 
[14800] 

700 
(170) 

375 

(1  10) 

240 
[600] 

[3270] 

[6130] 

B  for  H=i50     ...   | 

19200 

[18900] 

18800 
[19100] 

17400 
(15400) 

16700 
(11700) 

10400 
[nooo] 

[18200] 

[17550] 

4irl  for  saturation       .   j 

21620 

[21630] 

21420 
[21420] 

20600 
(20200) 

19800 
(18000) 

16400 

[16800] 

[20500] 

[19260] 

E.  Gumlich,  Zs.  fur  Electrochemie,  15,  p.  599;  1909. 
Brackets  indicate  annealing  at  800°  C  in  vacuum.  Parentheses  indicate  hardening  by  quenching  from  cherry-red. 

TABLE  299.  — Cast  Iron  in  Intense  Fields. 


Soft  Cast  Iron. 

Hard  Cast  Iron. 

H 

B 

I 

A* 

H 

B 

I 

P 

114 

9950 

782 

87.3 

142 

7860 

614 

554 

172 

10800 

846 

62.8 

254 

9700 

752 

38.2 

433 

13900 

1070 

32.1 

339 

10850 

836 

30.6 

744 

15750 

1  200 

21.2 

684 

13050 

983 

19.1 

1234 
1820 

17300 
18170 

1280 
1300 

14.0 
IO.O 

1570 

14050 
15900 

1044 
1138 

154 

IO.I 

12700 

31100 

1465 

2-5 

2O2O 

16800 

1146 

8-3 

13550 

32100 

'475 

2.4 

lOOXX) 

26540 

1235 

2.4 

13800 

32500 

1488 

2.4 

13200 

28600 

1226 

2.2 

15100 

33650 

1472 

2.2 

14800 

30200 

1226 

2.O 

B.  O.  Peirce,  Proc.  Am.  Acad.  44,  1909. 
TABLE  300.  —  Corrections  for  Ring  Specimens. 


hysteresis  is  less  than  it  would  be  for  a  uniform  distribution.  This  ratio  is  also  given 
for  the  case  of  constant  permeability,  the  values  being  applicable  for  magnetizations  in  the  neigh- 
borhood of  the  maximum  permeability.  For  higher  magnetizations  the  flux  density  is  more  uni. 
form,  for  lower  it  is  less,  and  the  correction  greater. 


SMITHSONIAN  TABLES. 


Ratio  of 
Radial 
Width  to 

Ratio  of  Average  H  to 
H  at  Mean  Radius. 

Ratio  of  Hysteresis  for  Uniform 
Distribution  to  Actual  Hysteresis. 

Diameter 
of  Ring. 

Rectangular 
Cross-section. 

Circular 
Cross-section. 

Rectangular 
Cross-section. 

Circular 
Cross-section. 

1/2 

1.0986 

1.0718 

1.  112 

1.084 

!//3 

1-0397 

1.0294 

1.045 

1.033 

i/4 

1.0216 

1.0162 

.024 

I.OlS 

i/5 

1.0137 

I.OIO2 

.015 

I.OII 

1/6 

1.0094 

1.0070 

.010 

1.008 

'/7 

1.0069 

1.0052 

.008 

1.  006 

1/8 

1.0052 

I.OO4O 

.006 

I.OO4 

I/IO 

1.0033 

I.OO25 

1.003 

I.OO2 

1/19 

1.0009 

1.0007 

1.  00  1 

1.  001 

M.  G.  Lloyd,  Bull.  Bur.  Standards,  5,  p.  415;  1908. 

TABLES  301,  302.  289 

DEMAGNETIZING  FACTORS  FOR  RODS. 
TABLE  301. 

H=  true  intensity  o*  magnetizing  field,  H'  =  intensity  of  applied  field,  /=  in- 
tensity of  magnetization,  H=  IP — NI. 

Shuddemagen  says :  The  demagnetizing  factor  is  not  a  constant,  falling  for 
highest  values  of  /to  about  1/7  the  value  when  unsaturated;  for  values  of  B 
(=&+4irS)  less  than  10000,  N  is  approximately  constant;  using  a  solenoid 
wound  on  an  insulating  tube,  or  a  tube  of  split  brass,  the  reversal  method  gives 
values  for  N  which  are  considerably  lower  than  those  given  by  the  step-by-step 
method  ;  if  the  solenoid  is  wound  on  a  thick  brass  tube,  the  two  methods  prac- 
tically agree. 


Values  of  NXio*. 

Cylinder. 

Ratio 
of 

Ballistic  Step  Method. 

Length 
to 
Diameter. 

Ellipsoid 

Uniform 
Magueti- 

Magneto- 
metric 
Method 

Dubois. 

Shuddemagen  for  Range  of 
Practical  Constancy. 

(Mann). 

Diameter. 

0.158  cm. 

0.3175  cm. 

i.  in  cm. 

1.905  cm. 

5 

7015 

_ 

6800 

IO 

2549 

630 

2550 

2l6o 

- 

- 

1960 

IS 

1350 

280 

I4OO 

1206 

— 

— 

1075 

20 

848 

160 

898 

775 

- 

- 

67I 

30 

43| 

70 

460 

393 

388 

350 

343 

40 

£ 

266 

181 
132 

39 

3 

274 
182 

131 

m 

118 

£ 

116 

212 

£ 

209 
149 
106 

70 

101 

13 

99 

89 

88 

80 

80 

9.8 

78 

69 

69 

66 

63 

90 

65 

7-8 

63 

55 

56 

100 

54 

6.3 

51.8 

45 

46 

4i 

4i 

150 

26 

2.8 

25.1 

20 

23 

21 

21 

2OO 

16 

i-57 

15.2 

II 

12.5 

II 

II 

300 

7-5 

0.70 

7-5 

5-g 

400 

4-5 

o-39 

2.8 

C.  R.  Mann,  Physical  Review,  3,  p.  359;  1896. 

H.  DuBois,  Wied.  Ann.  7,  p.  942 ;  1002. 

C.  L.  B.  Shuddemagen,  Proc.  Am.  Acad.  Arts  and  Sci.  43,  p.  185,  1907  (Bibliography). 


TABLE  302. 


Shuddemagen  also  gives  the  following,  where  B  is  determined  by  the  step  method 

andjy=#'— KB. 


Ratio  of 

Values  of  KX  10*. 

to 
Diameter. 

Diameter 
0.3175  cm. 

Diameter 
i.i  to  2.0  cm. 

IS 

_ 

85.2 

20 
25 

_ 

53-3 

36.6 

30 
40 

30-9 

1  8.6 

27-3 

16.6 

g 

12.7 
9.25 

1  1.6 

8-45 

80 

5>O5 

100 

3  66 

3  26 

150 

1.83 

1.67 

SMITHSONIAN  TABLES. 


290 


TABLE  303. 


COMPOSITION    AND   MAGNETIC 

This  table  and  Table  289  below  are  taken  from  a  paper  by  Dr.  Hopkinson  *  on  the  magnetic  properties  of  iron  and  steel. 
which  is  stated  in  the  paper  to  have  been  240.  The  maximum  magnetization  is  not  tabulated ;  but  as  stated  in  the 
by  4ir.  "  Coercive  force"  is  the  magnetizing  force  required  to  reduce  the  magnetization  to  zero.  The  '"demag- 
previous  magnetization  in  the  opposite  direction  to  the  "  maximum  induction"  stated  in  the  table.  The  "energy 
which,  however,  was  only  found  to  agree  roughly  with  the  results  of  experiment. 


1  

No. 
of 
Test 

Description  of 
specimen. 

Temper. 

Chemical  analysis. 

Total 
Carbon. 

Manga- 
nese. 

Sulphur. 

Silicon. 

Phos- 
phorus. 

Other 
substances. 

I 

Wrought  iron    . 

Annealed 

_ 

_ 

_ 

_ 

_ 

A 

2 

Malleaple  cast  iron   . 

" 

— 

— 

— 

— 

— 

— 

3 

Gray  cast  iron  . 

_ 

— 

— 

— 

— 

— 

— 

4 

Bessemer  steel  . 

_ 

0.045 

O.2OO 

0.030 

None. 

0.040 

_ 

5 

Whitworth  mild  steel 

Annealed 

0.090 

0.153 

0.016 

" 

0.042 

- 

!    6 

"               "               . 

" 

0.320 

0.438 

0.017 

0.042 

0-035 

-. 

(( 

(  Oil-hard- 

H 

M 

(t 

H 

7 

• 

|    ened 

8 

«               « 

Annealed 

0.890 

O.l65 

0.005 

0.081 

0.019 

- 

«               « 

(  Oil-hard- 

M 

(( 

u 

(( 

(( 

9 

• 

(    ened 

10 

Hadfield's  manganese  ) 
steel                           J    * 

- 

1.005 

12.360 

0.038 

0.204 

0.070 

- 

ii 

12 

Manganese  steel 

As  forged 
Annealed 

0.674 

4-730 

0.023 

0.608 

0.078 

: 

u               u 

(  Oil-hard- 

M 

H 

(t 

4< 

M 

*3 

(    ened 

14 

<(              it 

As  forged 

1.298 

8.740 

0.024 

0.094 

0.072 

~ 

15 

"              "             .         . 

Annealed 

II 

" 

" 

M 

/•• 

(  Oil-hard- 

(( 

(( 

» 

16 

• 

(    ened 

~ 

17 

Silicon  steel 

As  forged 

0.685 

0.694 

** 

3438 

0.123 

~ 

18 

"         "... 

Annealed 

" 

" 

" 

" 

_ 

(  Oil-hard- 

H 

« 

u 

(( 

L 

J9 

.        .        . 

\    ened 

* 

20 
21 

Chrome  steel    . 

As  forged 
Annealed 

0.532 

0-393 

O.O2O 

O.22O 

0.041 

H 

0.621  Cr. 

u 

(  Oil-hard- 

(( 

(( 

( 

(( 

t( 

22 

• 

(    ened 

23 
24 

«    ;     ;     ; 

As  forged 
Annealed 

0.687 
H 

O.O28 

!! 

0.134 

0.043 

1.195  Cr. 

(  Oil-hard- 

u 

25 

. 

(    ened 

" 

26 
27 

Tungsten  steel  . 

As  forged 
Annealed 

..357 

0.036 
tt 

None. 

0.043 

0.047 
H 

4.649  W. 
u 

C  Hardened 

28 

"           "... 

<    in  cold 

" 

" 

« 

« 

H 

« 

(    water 

^  Hardened 

29 

"           "... 

<    in  tepid 

It 

" 

« 

M 

" 

M 

(    water 

30 

"    (French)  . 

(  Oil-hard- 
{    ened 

0.5II 

0.625 

None. 

0.021 

0.028 

3.444  W. 

31 

1  32 

33 

Gray  cast  iron  . 
Mottled  cast  iron 

Very  hard 

0.855 

3455 
2.581 

0.312 
0-173 

0.610 

0.042 
0.105 

O.I5I 
2.044 
1.476 

0.089 
O.I5I 
0-435 

2.353  W. 
2.064  C.t 
1.477  C.t 

34 

White      "       " 

- 

2.036 

0.386 

0.467 

0.764 

0.458 

35 

Spiegeleisen 

4.510 

7.970 

Trace. 

0.502 

0.128 

*  Phil.  Trans.  Roy.  Soc.  vol.  176- 
SMITHSONIAN  TABLES. 


t  Graphitic  carbon. 


TABLE  303  (continued). 
PROPERTIES   OF   IRON   AND  STEEL. 


291 


The  numbers  in  the  columns  headed  "  magnetic  properties  "  give  the  results  for  the  highest  magnetizing  force  used, 
paper,  it  may  be  obtained  by  subtracting  the  magnetizing  force  (240)  from  the  maximum  induction  and  then  dividing 
netizing  force  "  is  the  magnetizing  force  which  had  to  be  applied  in  order  to  leave  no  residual  magnetization  after 
dissipated"  was  calculated  from  the  formula: — Energy  dissipated  =  coercive  force  X  maximum  induction  -j-  v 


No. 
of 
Test. 

Description  of 
specimen. 

Temper. 

Specific 
electri- 
cal resis- 
tance. 

Magnetic  properties. 

Energy  dis- 
sipated per 
cycle. 

Maxi- 
mum in- 
duction. 

Residual 
induc- 
tion. 

Coer- 
cive 
force. 

Demag- 
netizive 
force. 

I 

Wrought  iron   . 

Annealed 

.01378 

18251 

7248 

2.30 

_ 

13356 

2 

Malleable  cast  iron  . 

" 

•03254 

12408 

7479 

8.80 

— 

34742 

3 

Gray  cast  iron  . 

- 

.10560 

10783 

3928 

3.80 

- 

13037 

4 

Bessemer  steel  . 
Whitworth  mild  steel 

Annealed 

.01050 
.01080 

18196 
19840 

7860 
7080 

2.96 
1.63 

~ 

I7I37 
10289 

6 

«                « 

" 

.01446 

18736 

9840 

6-73 

- 

40120 

7 

<«                «< 

(  Oil-hard- 
(    ened 

.01390 

18796 

11040 

11.00 

- 

65786 

8 

«                «< 

Annealed 

•°I559 

l6l2O 

10740 

8.26 

- 

42366 

9 

«                « 

(  Oil-hard- 
(    ened 

.01695 

l6l2O 

8736 

19.38 

- 

99401 

10 

Hadfield's   manganese  ) 
steel                             J  ' 

- 

.06554 

3IO 

- 

- 

- 

ii 

12 

Manganese  steel 

«                          (4 

As  forged 
Annealed 

.05368 
.03928 

4623 
10578 

22O2 
5848 

23-50 

33-86 

37-13 
46.10 

34567 
113963 

*3 

«                         « 

(  Oil-hard- 
(    ened 

•05556 

4769 

2158 

27.64 

40.29 

41941 

H 

.    «                         « 

As  forged 

.06993 

747 

- 

- 

- 

- 

15 

«                          {« 

Annealed 

.06316 

1985 

540 

24.50 

5°-39 

15474 

16 

«                      M 

(  Oil-hard- 
(    ened 

.07066 

733 

- 

- 

- 

J7 

Silicon  steel 

As  forged 

.06163 

15148 

II073 

9-49 

12.60 

45740 

18 

H            « 

Annealed 

.06185 

14701 

8149 

7.80 

10.74 

36485 

19 

««            « 

(  Oil-hard- 
]    ened 

.06195 

14696 

8084 

12.75 

17.14 

59619 

20 

Chrome  steel     . 

As  forged 

.02016 

15778 

9318 

12.24 

13-87 

61439 

21 

«         « 

Annealed 

.01942 

14848 

7570 

8.98 

12.24 

42425 

22 

<«         « 

(  Oil-hard- 
(    ened 

.02708 

13960 

8595 

38-15 

48.45 

169455 

23 

««         <« 

As  forged 

.01791 

14680 

7568 

18.40 

22.03 

85944 

24 

«         « 

Annealed 

.01849 

13233 

6489 

15.40 

19.79 

64842 

25 

<«         « 

(  Oil-hard- 
(    ened 

•03035 

12868 

7891 

40.80 

56-70 

167050 

26 

Tungsten  steel  . 

As  forged 

.02249 

15718 

IOI44 

I5-7I 

1775 

78568 

27 

«           « 

Annealed 

.02250 

16498 

II008 

I5-30 

16.93 

80315 

Hardened 

28 

<«           «« 

in  cold 

.02274 

- 

- 

- 

- 

- 

water 

Hardened 

29 

«           « 

in  tepid 

.02249 

15610 

9482 

30.10 

34-70 

149500 

water 

3° 

"    (French)   . 

]  Oil  hard- 
(    ened 

.03604 

14480 

8643 

47.07 

64.46 

216864 

3i 

32 
33 

«           <« 

Gray  cast  iron    . 
Mottled  cast  iron 

Very  hard 

.04427 
.11400 
.06286 

12133 
9148 
10546 

68l8 
3l6l 

5108 

51.20 
13.67 
12.24 

70.69 
17.03 

197660 

39789 
41072 

34 

White        "       " 

- 

.05661 

9342 

5554 

12.24 

20.40 

36383 

35 

Spiegeleisen       .        .        . 

.10520 

77 

SMITHSONIAN  TABLES. 


292  TABLES  304-306. 

PERMEABILITY  OF  SOME   OF  THE   SPECIMENS   IN   TABLE    303. 

This  table  gives  the  induction  and  the  permeability  for  different  values  of  the  magnetizing  force  of  some  of  the  speci- 
mens in  Table  303.  The  specimen  numbers  refer  to  the  same  table.  The  numbers  in  this  table  have  been  taken 
from  the  curves  given  by  Dr.  Hopkinson,  and  may  therefore  be  slightly  in  error ;  they  are  the  mean  values  for 
rising  and  falling  magnetizations. 


Magnetiz- 
ing force. 
H 

Specimen  i  (iron). 

Specimen  8 
(annealed  steel). 

Specimen  9  (same  as 
8  tempered). 

Specimen  3 
(cast  iron). 

B 

M 

B 

M 

B 

V- 

B 

M 

I 

_ 

_ 

_ 

_ 

_ 

_ 

265 

265 

2 

200 

100 

— 

— 

— 

— 

700 

35° 

3 

- 

- 

- 

- 

- 

- 

1625 

542 

5 
10 

IOO5O 
12550 

2OIO 

1255 

1525 
9000 

300 
900 

750 
1650 

It? 

3000 
5OOO 

600 
500 

20 

14550 

727 

11500 

575 

5875 

294 

6OOO 

300 

3° 

I52OO 

5°7 

12650 

422 

9875 

329 

6500 

217 

40 

15800 

395 

13300 

332 

11600 

290 

7100 

177 

50 

I6000 

320 

13800 

276 

I2OOO 

240 

735° 

149 

70 

16360 

234 

J435o 

205 

13400 

191 

7900 

"3 

100 

16800 

168 

14900 

149 

I45OO 

145 

8500 

85 

150 

17400 

116 

15700 

105 

15800 

105 

9500 

63 

200 

17950 

90 

16100 

80 

l6lOO 

80 

10190 

51 

Tables  305-309  give  the  results  of  some  experiments  by  Du  Bois,*  on  the  magnetic  properties  of  iron,  nickel,  and 
cobalt  under  strong  magnetizing  forces.  The  experiments  were  made  on  ovoids  of  the  metals  18  centimetres  long 
and  0.6  centimetres  diameter.  The  specimens  were  as  follows:  (i)  Soft  Swedish  iron  carefully  annealed  and 
having  a  density  7.82.  (2)  Hard  English  cast  steel  yellow  tempered  at  230°  C. ;  density  7.78.  (3)  Hard  drawn 
best  nickel  containing  99  %  Ni  with  some  SiO2  and  traces  of  Fe  and  Cu ;  density  8.82.  (4)  Cast  cobalt  giving 
the  following  composition  on  analysis :  Co  :=  93.1,  Ni=  5.8,  Fe  —  0.8,  Cu  —  0.2,  Si  —  o. i,  and  C  —  0.3.  The  speci- 
men was  very  brittle  and  broke  in  the  lathe,  and  hence  contained  a  surfaced  joint  held  together  by  clamps  during 
the  experiment.  Referring  to  the  columns,  ff,  B,  and  fj.  have  the  same  meaning  as  in  the  other  tables,  .5"  is  the 
magnetic  moment  per  gramme,  and  7  the  magnetic  moment  per  cubic  centimetre.  H  and  6"  are  taken  from  the 
curves  published  by  Du  Bois ;  the  others  have  been  calculated  using  the  densities  given. 

TABLE  305. 

MAGNETIC    PROPERTIES    OF    SOFT    IRON    AT    O     AND    1 0O     C. 


Soft  iron  at  o°  C. 

Soft  iron  at  100°  C. 

H 

S 

/ 

B 

V- 

H 

S 

/ 

B 

M 

100 

1  80.0 

1408 

17790 

177.9 

100 

iSo.O 

I4O2 

17720 

177.2 

200 

194-5 

I52I 

19310 

9^5 

2OO 

194.0 

'S11 

19190 

96.0 

400 

2O8.O 

1627 

20830 

52.1 

400 

207.0 

1613 

20660 

51.6 

700 

2X<?.5 

1685 

21870 

31.2 

700 

213.4 

1663 

21590 

29.8 

IOOO 

215.0 

1705 

22420 

22.4 

IOOO 

215.0 

1674 

22040 

2I.O 

1200 

218.5 

1709 

22670 

18.9 

I2OO 

215-5 

1679 

22300 

18.6 

TABLE  306. 

MAGNETIC    PROPERTIES    OF    STEEL    AT    O°    AND    10O°    C. 


Steel  at  o°  C. 

Steel  at  100°  C. 

H 

S 

/ 

B 

M 

H 

S 

/ 

B 

V- 

100 

165.0 

1283 

16240 

162.4 

100 

165.0 

1278 

16170 

161.7 

200 

181.0 

1408 

17900 

89-5 

2OO 

iSo.O 

1395 

17730 

88.6 

400 

193.0 

1500 

19250 

48.1 

400 

I9I.O 

1480 

19000 

47-5 

700 

199-5 

1552 

20210 

28.9 

700 

197.0 

1527 

19890 

28.4 

IOOO 

203-5 

1583 

20900 

20.9 

IOOO 

199.0 

1543 

20380 

20.4 

I2OO 

375°t 

205.0 

2I2.O 

1595 
1650 

2I24O 
24470 

17.7 

6-5 

1500 

3000 

5000 

203.0 

205-5 
208.0 

1573 
1593 

1612 

21270 
23020 
25260 

14.2 
7-7 
5-i 

"  Phil.  Mag."  5  series,  vol.  xxix. 

t  The  results  in  this  and  the  other  tables  for  forces  above  1200  were  not  obtained  from  the  ovoids  above  referred 
to,  but  from  a  small  piece  of  the  metal  provided  with  a  polished  mirror  surface  and  placed,  with  its  polished  face  nor- 
mal to  the  lines  of  force,  between  the  poles  of  a  powerful  electromagnet.  The  induction  was  then  inferred  from 
the  rotation  of  the  plane  of  a  polarized  ray  of  red  light  reflected  normally  from  the  surface.  (See  Kerr's  "Constants," 
p.  292.) 


TABLES  307-313. 

MAGNETIC    PROPERTIES    OF    METALS. 
TABLE  307.  -  Cobalt  at  100°  0.  TABLE  308.  -Nickel  at  100°  0. 


293 


H 

S 

7 

B 

p 

2OO 

106 

848 

10850 

54-2 

300 

116 

928 

11960 

39-9 

500 

127 

1016 

13260 

26.5 

700 

1048 

13870 

19.8 

IOOO 

134 

1076 

14520 

14-5 

1500 

138 

1104 

15380 

10.3 

2500 

143 

"44 

16870 

6.7 

4000 

'45 

1164 

18630 

4-7 

6000 

1176 

20780 

9000 

149 

1192 

23980 

2.6 

At  o°  C.  this  specimen  gave  the  fol- 

lowing results  : 

7900 

1232  )  23380 

3-0 

H 

S 

7 

B 

M 

100 

35-o 

3°9 

398o 

39-8 

200 

43-o 

380 

4966 

24.8 

300 

46.0 

406 

5399 

18.0 

500 

50.0 

441 

6043 

12.1 

700 

Si-5 

454 

6409 

9.I 

IOOO 

53-° 

468 

6875 

6.9 

1500 

56.0 

494 

7707 

5-i 

2500 

58.4 

5i5 

8973 

3-6 

4000 

59-° 

520 

10540 

2.6 

6000 

59-2 

522 

12561 

2.1 

9000 

59-4 

524 

15585 

i-7 

I2OOO 

At  o°  C 

59-6 
.  this  sj 

526 
Decimer 

gave  th 

e  fol- 

12300 

lowi 
67.5 

ng  results  : 
595  I  19782 

1.6 

TABLE  309.— Magnetite. 

The  following  results  are  given  by  Du  Bois  *  for  a  specimen  of  magnetite. 


H 

7 

B 

M 

500 
IOOO 
2000 
I2OOO 

325 

345 
350 
350 

8361 
9041 
10084 
20084 

I6.7 
9-0 

5-o 
i-7 

Professor  Ewing  has  investigated  the  effects  of  very  intense  fields  on  the  induction  in  iron  and  other  metals.f  The 
results  show  that  the  intensity  of  magnetization  does  not  increase  much  in  iron  after  the  field  has  reached  an  in- 
tensity of  looo  c.  g.  s.  units,  the  increase  of  induction  above  this  being  almost  the  same  as  if  the  iron  were  not 
there,  that  is  to  say,  dBj  dff  is  practically  unity.  For  hard  steels,  and  particularly  manganese  steels,  much  higher 
forces  are  required  to  produce  saturation.  Hadfield's  manganese  steel  seems  to  have  nearly  constant  susceptibility 
up  to  a  magnetizing  force  of  10,000.  The  following  tables,  taken  from  E  wing's  papers,  illustrate  the  effects  of 
strong  fields  on  iron  and  steel.  The  results  for  nickel  and  cobalt  do  not  differ  greatly  from  those  given  above. 


TABLE  310.  —  Lowmoor 
Wrought  Iron. 


TABLE  311.  — Vlcker's 
Tool  Steel. 


TABLE  312.  -  Hadfield's 
Manganese  Steel. 


H 

7 

B 

P 

3080 
6450 
10450 
13600 
16390 
18760 
18980 

1680 
1740 

173° 
1720 
1630 
1680 
173° 

24130 
28300 
32250 
35200 
36810 
39900 
40730 

7.83 

4-39 
3-09 
2-59 
2.25 
2.13 
2.15 

H 

7 

B 

I 

6210 

1530 

25480 

4.10 

9970 

1570 

29650 

2.97 

I2I2O 

1550 

31620 

2.6o 

14660 
15530 

I|80 

1610 

34550 
35820 

2.36 
2.3I 

H 

7 

B 

> 

1930 

55 

2620 

1.36 

2380 

84 

343° 

1.44 

3350 

84 

4400 

i-3« 

5920 

in 

73*o 

1.24 

6620 

187 

8970 

!-35 

7890 

191 

10290 

1.30 

8390 
9810 

3 

11690 
14790 

i-39 
i-5i 

TABLE  313. -Saturation  Values  for  Steels  of  Different  Kinds. 


H 

7 

B 

M 

I 

2 

3 

Bessemer  steel  containing  about  0.4  per  cent  carbon  .     .     . 
Siemens-Marten  steel  containing  about  0.5  per  cent  carbon 
Crucible  steel  for  making  chisels,  containing  about  0.6  per 
cent  carbon     

17600 
18000 

IQ47O 

1770 
1660 

1480 

39880 
38860 

38010 

2.27 
2.16 

i.qq 

4 

c 

Finer  quality  of  3  containing  about  0.8  per  cent  carbon  .     . 
Crucible  steel  containing  I  per  cent  carbon             .... 

18330 

1580 
I44O 

38190 

776QO 

2.6*5 
I.Q2 

1 

^^hitworth's  fluid-compressed  steel                 .                   . 

I87OO 

I  <*QO 

•28710 

2.  07 

*  "  Phil.  Mag."  5  series,  vol.  xxix. 


t  "  Phil.  Trans.  Roy.  Soc."  1885  and  1889. 


294  TABLES  31 4-31  6. 

TABLE  314.-MAGNETIC   PROPERTIES   OF  IRON    IN  VERY  WEAK   FIELDS. 

The  effect  of  very  small  magnetizing  forces  has  been  studied  by  C.  Baur  *  and  by  Lord  Rayleigh.t  The  following 
short  table  is  taken  from  Baur's  paper,  and  is  taken  by  him  to  indicate  that  the  susceptibility  is  finite  for  zero  values 
of  H  and  for  a  finite  range  increases  in  simple  proportion  to  H.  He  gives  the  formula  k=  15  +  100  //,  or  I  — 
15  ff-\- 100  //2.  The  experiments  were  made  on  an  annealed  ring  of  round  bar  1.013  cms.  radius,  the  nng  having 
a  radius  of  9.432  cms.  Lord  Rayleigh's  results  for  an  iron  wire  not  annealed  give  k  —  6.4  +  5-1  H,  or  /  =  6.4  H 
4-5.1  //2.  The  forces  were  reduced  as  low  as  0.00004  c.  g.  s.,  the  relation  of  k  to  H  remaining  constant. 


First  experiment. 

Second  experiment. 

H 

k 

/ 

H 

k 

.01  580 

16.46 

2.63 

.0130 

T5-5° 

.03081 
.07083 

17-65 
23.00 

5-47 
l6-33 

.0847 
.0946 

18.38 
20.49 

.13188 

28.90 

38-15 

.1864 

25.07 

.23011 

.38422 

39.81 
58.56 

91.56 
224.87 

.2903 

•3397 

32.40 
35.20 

TABLES  315,  316.-DISSIPATION  OF  ENERGY  IN  CYCLIC  MAGNETIZATION 
OF  MAGNETIC  SUBSTANCES. 

When  a  piece  of  iron  or  other  magnetic  metal  is  made  to  pass  through  a  closed  cycle  of 
magnetization  dissipation  of  energy  results.  Let  us  suppose  the  iron  to  pass  from  zero  magneti- 
zation to  strong  magnetization  in  one  direction  and  then  gradually  back  through  zero  to  strong 
magnetization  in  the  other  direction  and  thence  back  to  zero,  and  this  operation  to  be  repeated 
several  times.  The  iron  will  be  found  to  assume  the  same  magnetization  when  the  same  magne- 
tizing force  is  reached  from  the  same  direction  of  change,  but  not  when  it  is  reached  from  the 
other  direction.  This  has  been  long  known,  and  is  particularly  well  illustrated  in  the  permanency  of 
hard  steel  magnets.  That  this  fact  involves  a  dissipation  of  energy  which  can  be  calculated  from 
the  open  loop  formed  by  the  curves  giving  the  relation  of  magnetization  to  magnetizing  force  was 
pointed  out  by  Warburg  \  in  1881,  reference  being  made  to  experiments  of  Thomson,  §  where  such 
curves  are  illustrated  for  magnetism,  and  to  E.  Cohn,  ||  where  similar  curves  are  given  for  thermo- 
electricity. The  results  of  a  number  of  experiments  and  calculations  of  the  energy  dissipated 
are  given  by  Warburg.  The  subject  was  investigated  about  the  same  time  by  Ewing,  who  pub- 
lished results  somewhat  later.  T  Extensive  investigations  have  since  been  made  by  a  number  of 
investigators. 


TABLE  315.-  Soft  Iron  Wire. 

(From  Ewing's  1885  paper.) 


Horse- 

Total 
induction 

Dissipation 
of  energy 

power 
wasted  per 

per  sq.  cm. 
B 

in  ergs  per 
cu.  cm. 

ton  at  100 
cycles  per 

sec. 

2000 

420 

0.74 

3000 

800 

I.4I 

4000 

1230 

2.18 

5000 

1700 

3.01 

6OOO 

22OO 

3-89 

7000 

2760 

4-88 

8000 

3450 

6.10 

9OOO 

42OO 

7-43 

1  0000 

5000 

8.84 

1  1000 

582O 

10.30 

I2OOO 

6720 

11.89 

13000 

7650 

13-53 

14000 

8650 

I5-30 

I5OOO 

9670 

17^10 

TABLE  316.  —  Cable  Transformers. 

This  table  gives  the  results  obtained  by  Alexander  Siemens  with  one  of 
Siemens'  cable  transformers.  The  transformer  core  consisted  of  900 
soft  iron  wires  i  mm.  diameter  and  6  metres  long.**  The  dissipation 
of  energy  in  watts  is  for  100  complete  cycles  per  second. 


Mean  maxi- 
mum induc- 
tion density 
in  core. 
B 

Total  ob- 
served  dis- 
sipation of 
energy  in  the 
core  in  watts 
per  H2  Ibs. 

Calculated 
eddy  current 
loss  in  watts 
per  112  Ibs. 

Hysteresis 
loss  of 
energy  in 
watts  per 
1  12  Ibs. 

Hysteresis 
loss  of 
energy  in 
ergs  per 
cu.  cm. 
per  cycle. 

1000 

43-2 

4 

39-2 

602 

2000 

96.2 

16 

80.2 

1231 

3OOO 

158.0 

36 

122.0 

1874 

4000 

231.2 

64 

167.2 

2566 

5000 

309-5 

100 

209.5 

3217 

6OOO 

390.1 

144 

246.1 

3779 

*  "  Wied.  Ann."  vol.  xi.  t  "  Phil.  Mag."  vol.  xxiii. 

$  "  Wied.  Ann."  vol.  xiii.  p.  141.  §  "  Phil.  Trans.  Roy.  Soc."  vol.  175. 

II  "  Wied.  Ann."  vol.  6.  1  "  Proc.  Roy.  Soc.1'  1882,  and  "  Trans.  Roy,  Soc."  1885. 

**  "  Proc.  Inst.  of  Elect.  Eng."  Lond.,  1892. 
SMITHSONIAN  TABLES. 


TABLE  317. 


295 


DISSIPATION  OF  ENERGY  IN  THE  CYCLIC  MAGNETIZATION  OF  VARIOUS 

SUBSTANCES. 

C.  P.  Steinmetz  concludes  from  his  experiments  *  that  the  dissipation  of  energy  due  to 
hysteresis  in  magnetic  metals  can  be  expressed  by  the  formula  e  =  a£1-6,  where  e  is  the  energy 
dissipated  and  a  a  constant.  He  also  concludes  that  the  dissipation  is  the  same  for  the  same 
range  of  induction,  no  matter  what  the  absolute  value  of  the  terminal  inductions  may  be.  His 
experiments  show  this  to  be  nearly  true  when  the  induction  does  not  exceed  -^-  15000  c.  g.  s. 
units  per  sq.  cm.  It  is  possible  that,  if  metallic  induction  only  be  taken,  this  may  be  true  up  to 
saturation  ;  but  it  is  not  likely  to  be  found  to  hold  for  total  inductions  much  above  the  satura- 
tion value  of  the  metal.  The  law  of  variation  of  dissipation  with  induction  range  in  the  cycle, 
stated  in  the  above  formula,  is  also  subject  to  verification.! 


Values  of  Constant  a. 

The  following  table  gives  the  values  of  the  constant  a  as  found  by  Steinmetz  for  a  number  of  different  specimens* 
The  data  are  taken  from  his  second  paper. 


Number  of 
specimen. 

Kind  of  material. 

Description  of  specimen. 

Value  of 
a. 

I 

Iron 

Norway  iron     

.00227 

2 

« 

Wrought  bar     

.00326 

-i 

<< 

.OO54.8 

O 

4 

<( 

Annealed            "            "          

•W^TJJ 
OO4c8 

*T 

C 

« 

Thin  tin  plate    

•MWl^VJ 

.OO286 

6 

« 

Medium  thickness  tin  plate       

.00425 

• 

Steel 

.OO74Q 

0 

« 

^||T'Jf 

.00848 

q 

H 

OO4.57 

:? 
IO 

« 

•v-"-"+j/ 
.OO7I8 

II 

« 

Same  as  8  tempered  in  cold  water   .... 

.02792 

12 

M 

Tool  steel  glass  hard  tempered  in  water 

.07476 

11 

« 

.02670 

*  J 
14 

M 

«        "      annealed  

.01899 

IS 

? 

(  Same  as  12,  1  3,  and  14,  after  having  been  subjected  ) 

(  .06130 

16 

[ 

<  to   an  alternating  m.  m.  f.  of  from  4000  to  6000  > 

1  .02700 

17 

) 

(  ampere  turns  for  demagnetization    .        .        .        .  ) 

(  •QI44S 

Y  Q 

Cast  iron 

19 

«        « 

"        "      "    containing  |  %  aluminium 

.01365 

20 

«        « 

«      «     <«           «       i  v        " 

.0,1459 

(  A  square  rod  6  sq.  cms.  section  and  6.5  cms.  long,  ) 

21 

Magnetite  . 

<  from   the  Tilly  Foster  mines,  Brewsters,   Putnam  > 
(  County,  New  York,  stated  to  be  a  very  pure  sample  ) 

.02348 

22 

Nickel 

.0122 

M 

(  Annealed    wire,    calculated    by    Steinmetz    from  ) 

ff 

23 

|  Ewing's  experiments         ) 

.0150 

24 

« 

Hardened,  also  from  Ewing's  experiments 

•0385 

25 

Cobalt       . 

(  Rod  containing  about  2  %  of  iron,  also  calculated  ) 
j  from  Ewing's  experiments  by  Steinmetz          .        .  J 
Consisted  of  thin   needle-like  chips  obtained  by 

.0120 

milling  grooves  about  8  mm.  wide  across  a  pile  of 

thin  sheets  clamped  together.     About  30  %  by  vol- 

26 

Iron  filings 

ume  of  the  specimen  was  iron, 
ist  experiment,  continuous  cyclic  variation  of  m.  m.  ) 
f.  1  80  cycles  per  second    J 

•0457 

2d  experiment,  114  cycles  per  second 

.0396 

3d          "            79-91  cycles  per  second  . 

•°373 

*  "  Trans.  Am.  Inst.  Elect.  Eng."  January  and  September,  1893 
t  See  T.  Gray,  "  Proc.  Roy.  Soc."  vol.  Ivi 


SMITHSONIAN  TABLES. 


296 


TABLE  318. 
ENERGY  LOSSES  IN  TRANSFORMER  STEELS, 


Determined  by  the  wattmeter  method. 

Loss  per  cycle  per  cc  =  AB*-\-bnBv,  where  B  =  flux  density  in  gausses  and  n  =  frequency  in 

cycles  per  second,  x  shows  the  variation  of  hysteresis  with  B  between  5000  and  10000  gausses, 

and  y  the  same  for  eddy  currents. 


Ergs  per  Gramme  per  Cycle. 

Watts  per  Pound  at  60  Cy- 

cles and  i  oooo  Gausses. 

Thick- 

loooo Gausses. 

5000  Gausses. 

c  & 

Designation. 

ness. 

x 

y 

a 

IL 

Hyste- 
resis. 

|fc 

Hyste- 
resis. 

Jf. 

K** 

Hyste- 
resis. 

Total. 

Unannealed 

A 

0.0399 

'599 

186 

562 

46 

I'5I 

2.02 

0.00490 

0.4I 

4-35 

4.76 

B 

.0326 

1156 

'34 

36 

1-59 

1.89 

.00358 

0.44 

3-58 

C 

.0422 

1032 

242 

356 

70 

'•51 

1.79 

•00319 

0.47 

2.81 

3.28 

D 

.0381 

1009 

184 

353 

48 

1.52 

1.94 

.00312 

0.44 

2.74 

3.18 

Annealed 

E 
F 

.0476 
.0280 

K 

236 

100 

246 

220 

58 
27 

\'.£ 

2.02 

1.88 

.00227 
.00206 

0.36 

0.44 

2.00 

1.81 

2.36 

2.25 

G 
H* 

•0394 
.0307 

563 
412 

2IO 
I46 

193 
138.5 

54 
39 

1.54 

.96 
•90 

.00174 
.00127 

0.47 
0-54 

1.  12 

2.00 

1.66 

i. 

.0318 
.0282 

341 

394 

202 
124 

III.5 
130 

55 
32 

i!6i 

.88 

.00105 
.00122 

0.70 
0-54 

0-93 
1.07 

1.63 
1.61 

L 

.0346 

38i 

I84 

I25 

5° 

1.61 

.88 

.OOIlS 

0-535 

1-035 

1.57 

B 

.0338 

354 

200 

116 

57 

1.61 

.81 

.00110 

0.6  1 

0.96 

1.57 

M 

.0335 

372 

I78 

127 

46 

1.55 

•95 

.00115 

o«55 

I.OI 

1.56 

N 

.0340 

321 

210 

105 

56 

1.62 

.90 

.00099 

0.63 

0.87 

1.50 

P 

•0437 

334 

I84 

107 

50 

1.64 

.88 

.00103 

0-34 

0.91 

1.25 

Silicon  steels 

Qt 

.0361 

3°3 

54 

98 

15 

1.63 

- 

.00094 

0.14 

0.825 

0.965 

R 

•°3  i  5 

288 

42 

93 

ii 

1.64 

- 

.00089 

0.15 

0.78 

0-93 

S 

.0452 

278 

72 

90 

18 

1.63 

— 

.00086 

O.I  2 

0-755 

0.875 

5 

•0338 
.0346 

250 
270 

60 
42 

1 

18 

12 

i!f56 

: 

.00077 
.00084 

0.18 

0.12 

0.68 
0-735 

0.86 
0-855 

v* 

.0310 

25I-5 

47 

79 

13 

1.68 

~ 

.00078 

0.17 

0.685 

0.855 

w* 

•0305 

197 

43 

62.3 

12.4 

1.67 

— 

.0006l 

0.16 

0-535 

0.695 

X 

.0430 

200 

65 

64.2 

16.6 

1.65 

.00062 

0.12 

0-545 

0.665 

*  German.  t  English. 

t  In  order  to  make  a  fair  comparison,  the  eddy  current  loss  has  been  computed  for  a  thickness  of  0.0357  cm.  (Gage 
No.  29),  assuming  the  loss  proportional  to  the  thickness. 

Lloyd  and  Fisher,  Bull.  Bur.  Standards,  5,  p.  453 ;  1909. 
SMITHSONIAN    TABLES. 


TABLE  31  9.  297 

MAGNETO-OPTIC  ROTATION. 

Faraday  discovered  that,  when  a  piece  of  heavy  glass  is  placed  in  magnetic  field  and  a  beam 
of  plane  polarized  light  passed  through  it  in  a  direction  parallel  to  the  lines  of  magnetic  force, 
the  plane  of  polarization  of  the  beam  is  rotated.  This  was  subsequently  found  to  be  the  case 
with  a  large  number  of  substances,  but  the  amount  of  the  rotation  was  found  to  depend  on  the 
kind  of  matter  and  its  physical  condition,  and  on  the  strength  of  the  magnetic  field  and  the 
wave-length  of  the  polarized  light.  Verdet's  experiments  agree  fairly  well  with  the  formula  — 


where  c  is  a  constant  depending  on  the  substance  used,  /  the  length  of  the  path  through  the 
substance,  H  the  intensity  of  the  component  of  the  magnetic  field  in  the  direction  of  the  path 
of  the  beam,  r  the  index  of  refraction,  and  A.  the  wave-length  of  the  light  in  air.  If  H  be  dif- 
ferent, at  different  parts  of  the  path,  Iff  is  to  be  taken  as  the  integral  of  the  variation  of  mag- 
netic potential  between  the  two  ends  of  the  medium.  Calling  this  difference  of  potential  z/,  we 
may  write  Q  —  Av,  where  A  is  constant  for  the  same  substance,  kept  under  the  same  physical 
conditions,  when  the  one  kind  of  light  is  used.  The  constant  A  has  been  called  "  Verdet's  con- 
stant," *  and  a  number  of  values  of  it  are  given  in  Tables  303-310.  For  variation  with  tempera- 
ture the  following  formula  is  given  by  Bichat  :  — 

R  =  RQ  (i—  0.00104^—0.000014/2), 

which  has  been  used  to  reduce  some  of  the  results  given  in  the  table  to  the  temperature  corre- 
sponding to  a  given  measured  density.  For  change  of  wave-length  the  following  approximate 
formula,  given  by  Verdet  and  Becquerel,  may  be  used  :  — 


•»    /vW-'K" 

where  /t  is  index  of  refraction  and  \  wave-length  of  light. 

A  large  number  of  measurements  of  what  has  been  called  molecular  rotation  have  been  made, 
particularly  for  organic  substances.  These  numbers  are  not  given  in  the  table,  but  numbers 
proportional  to  molecular  rotation  may  be  derived  from  Verdet's  constant  by  multiplying  in  the 
ratio  of  the  molecular  weight  to  the  density.  The  densities  and  chemical  formulae  are  given  in 
the  table.  In  the  case  of  solutions,  it  has  been  usual  to  assume  that  the  total  rotation  is  simply 
the  algebraic  sum  of  the  rotations  which  would  be  given  by  the  solvent  and  dissolved  substance, 
or  substances,  separately  ;  and  hence  that  determinations  of  the  rotary  power  of  the  solvent 
medium  and  of  the  solution  enable  the  rotary  power  of  the  dissolved  substance  to  be  calculated. 
Experiments  by  Quincke  and  others  do  not  support  this  view,  as  very  different  results  are 
obtained  from  different  degrees  of  saturation  and  from  different  solvent  media.  No  results  thus 
calculated  have  been  given  in  the  table,  but  the  qualitative  result,  as  to  the  sign  of  the  rotation 
produced  by  a  salt,  may  be  inferred  from  the  table.  For  example,  if  a  solution  of  a  salt  in  water 
gives  Verdet's  constant  less  than  0.0130  at  20°  C.,  Verdet's  constant  for  the  salt  is  negative. 

The  table  has  been  for  the  most  part  compiled  from  the  experiments  of  Verdet,t  H.  Becque- 
rel,J  Quincke,  §  Koepsel,||  Arons,1[  Kundt,**  Jahn,tt  Schonrock,JJ  Gordon,  §§  Rayleigh  and 
Sidgewick,||||  PerkinJ!  Bichat.*** 

As  a  basis  for  calculation,  Verdet's  constant  for  carbon  disulphide  and  the  sodium  line  D  has 
been  taken  as  0.0420  and  for  water  as  0.0130  at  20°  C. 

*  The  constancy  of  this  quantity  has  been  verified  through  a  wide  range  of  variation  of  magnetic  field  by  H.  £ 
J.  G.  Du  Bois  (Wied.  Ann.  vol.  35). 

t    'Ann.  de  Chim.  et  de  Phys."  [3]  vol.  52. 

Ann.  de  Chim.  et  de  Phys."  [5]  vol.  12  ;  "  C.  R."  vols.  90  and  100. 


Wied.  Ann. 
Wied.  Ann. 
Wied.  Ann. 
Wied.  Ann. 
Wied.  Ann. 


vol.  24. 
vol.  26. 
vol.  24. 

vols.  23  and  27. 
vol.  43. 


Zeits.  fur  Phys.  Chem."  vol.  n. 
Proc.  Roy.  Soc."  1883. 
Phil.  Trans.  R.  S."  1885. 
Jour.  Chem.  Soc."  vols.  8  and  : 
Jour,  de  Phys."  vols.  8  and  9. 


SMITHSONIAN  TABLES. 


TABLE  320. 
MAGNETO-OPTIC  ROTATION. 

Solids. 


Substance. 

Chemical 
formula. 

Density 
or 
grammes 
per  c.  c. 

Kind 
of 
light. 

Verdet's 
constant 
in 
minutes. 

Temp.  C. 

Authority. 

Amber      
Blende      

ZnS 

- 

D 
it 

0.0095 

O  22  7A 

18-20° 
T  r 

Quincke. 

c 

» 

o  0127 

lj 
« 

« 

Fluor  spar        .        .        . 

CaFl2 

- 

« 

0.0087 

« 

M 

Glass  : 

« 

o  020^ 

H 

« 

Faraday  A    .... 

- 

5458 

«< 

0.0782 

1  8-20 

Quincke. 

B    . 
Flint      

- 

4.284 

« 
« 

0.0649 

« 
«( 

M 

« 

u 

« 

o  0^2  c 

T  r 

«« 

« 

w'wo^:> 
o  0416 

*J 
ft 

« 

"      dense  .... 

- 

- 

K 

0.0576 

<( 

« 

t(         <t 
Plate      

- 

- 

« 
« 

0.0647 
o  0406 

u 

1  8—  20 

«« 

Lead  borate      .... 

PbB204 

- 

« 

0.0600 

r5 

Becquerel. 

Quartz  (perpendicular  to  axis) 

- 

- 

« 

0.0172 

18-20 

Quincke. 

Rock  salt          .... 

NaCl 

- 

« 

0.0355 

15 

Becquerel. 

Selenium  

Se 

- 

B 

0.4625 

«« 

« 

Sodium  borate 

Na2B407 

- 

D 

0.0170 

« 

« 

Spinel  (colored  by  chrome) 

- 

- 

« 

0.0209 

« 

« 

Sylvine     

KC1 

- 

« 

0.0283 

« 

• 

Ziqueline  (suboxide  of  copper) 

Cu2O 

- 

B 

0.5908 

u 

« 

SMITHSONIAN  TABLES. 


TABLE  321 . 

MAGNETO-OPTIC   ROTATION. 

Liquids. 


299 


Substance. 

Chemical 
formula. 

Density 
in 
grammes 
per  c.  c. 

Kind 
of 
light. 

Verdet's 
constant 
in 
minutes. 

Temp. 
C. 

Authority. 

Acetone    

C8H6O 

« 

0.7947 
O.7CK7 

D 

O.OII3 
0.0115 

20 
I  c 

Jahn. 
Perkin. 

M 

Acids  :    (see  also  solutions  in 
water) 

« 
C2H4O2 

0.7947 
I.O56l 

« 

« 

O.OII4 
O.OIO5 

it 

21 

Schonrock. 
Perkin. 

Butyric  

C4H802 
CH2O2 

0.9663 

1.2277 

« 
« 

0.0116 
0.0105 

15 
I  c 

«< 

Hydrochloric 

M 

Hydrobromic 
Hydroiodic   .... 

HC1 

HBr 
HI 
HNO8 

1.2072 
I-7859 

1-9473 

I.C.IQO 

« 

tt 
« 
« 

M 

0.0224 
0.0206 
0.0343 
0.0513 
0.0070 

IS 

IS 

15 
15 

17 

«< 

Becquerel. 
Perkir. 

H 
<« 

"      (fuming)      . 
Propionic      .... 
Sulphuric      .... 
Sulphurous   .... 
Valeric           .... 

C3H6O2 
H2S04 
H2S08 
CsHioO-j 

0-9975 

0.0418 

«« 
« 
M 
<« 
« 

0.0080 

O.OIIO 
O.OI2I 
0.0153 
O.OI2I 

'5 
i5 
iS 
15 

I  c 

Becquerel. 
Perkin. 

Becquerel. 
« 

Perkin. 

Alcohols  : 
Amyl     

C6HnOH 

« 

O.8lO7 

« 
H 

O.OI3I 
O.OI28 

1  J 

15 

20 

Becquerel. 
Jahn. 

Butyl     
« 

C4H9OH 

M 

0.802  1 

« 
« 

O.OI24 

o.oi  24 

20 

T  C 

<( 

Ethyl     

C2H5OH 

O.7Q2Q 

(« 

0.0107 

1  J 

18-20 

Ouincke. 

M 

O.7QOO 

M 

O.OI  12 

2O 

Jahn 

« 

« 

O.7Q4.4. 

<« 

O.OII4 

I  r 

Perkin 

« 

Methyl  

« 
CH3OH 

0-7943 
0.701  c, 

«< 

(1 

O.OII3 
O.OO94 

16 
18-20 

Schonrock. 
Ouincke. 

0.7020 

M 

O.OOQ7 

20 

Jahn. 

« 

« 

« 

o.oi  06 

J  C 

Becquerel 

« 
« 

« 
« 

0.7966 
0.7007 

« 
« 

0.0096 
0.0096 

15 

21.  Q 

Perkin. 
Schonrock 

Octyl     

C8H17OH 

0.8296 

« 

O.OI  14. 

1C 

Perkin 

C3H7OH 

0.8050 

<« 

O.OI  2O 

2O.8 

Schonrock 

<t 

M 

0.8082 

«< 

O.OI  2O 

I  c  o 

Perkin 

« 
« 

(« 

0.8042 

«< 

O.OIlS 
O.OI  2O 

15 
2O 

Becquerel. 
Jahn 

C6H6 

0.8786 

«< 

O.O2O7 

2O 

Jahn 

N 

« 

«< 

O.O268 

1C 

« 

«« 

08718 

«( 

O.O3OI 

26  9 

Bromides  : 
Bromoform  .... 
Ethyl     

CHBr3 
C2H5Br 

2.9021 
1.4486 

« 

« 

0.0317 
0.0183 

IS 

I  e 

Perkin. 
« 

Ethylene       .... 
« 

Methyl.        '.        '.        '.        ! 
Methylene     .... 
Octyl     

C2H4Br2 
n 

CH3Br 
CH2Br2 
C8H17Br 

2.1871 
2.1780 

I-733I 
2.4971 
1.1170 

«< 
«( 

« 
• 
« 

0.0268 
0.0269 
O.O2O5 
0.0276 
0.0164 

IS 
2O 
0 

15 

I  c 

«< 

Jahn. 

Perkin. 

« 

«i 

Propyl  
Carbon  disulphide   . 
«              « 

tt              « 
«<              « 
««              « 
«i              «< 

C3H7Br 
CS2 
« 

H 
«« 
« 
«« 

1.3600 
1.2644 

M 

« 

« 

H 
M 
« 
«« 

O.OlSo 
0.0441 

0.0434 

0.0433 
O.O42O 
0.0420 
0.0439 

18-20 

0 

o 
18 
18 

0 

« 

Quincke. 
(  Becquerel, 
i      1885. 
Gordon. 
Rayleigh. 
Koepsel. 
Arons. 

SMITHSONIAN  TABLES. 


3oo 


TABLE  321  (continued). 


MAGNETO-OPTIC  ROTATION, 

Liquids. 


Substance. 

Chemical 
formula. 

Density 
in 
grammes 
per  c.  c. 

Kind 
of 
light. 

Verdet's 
constant 
in 
minutes. 

Temp. 

Authority. 

Chlorides  : 

CHC1 

o  874.0 

D 

O.OI4O 

John 

Arsenic 

As 

\j.uj  tyj 

u 

0.0422 

15 

j  tin  u. 

Becquerel. 

Carbon 

c 

mm 

" 

0.0170 

15 

« 

"       bichloride 

CC14 

_ 

it 

0.0321 

I  c 

« 

Chloroform 

CHC18 

1.4823 

" 

0.0164 

J 

20 

Jahn. 

"          ... 

H 

1.4990 

M 

0.0166 

1C 

Perkin. 

Ethyl  .... 

C2H6C1 

o  0160 

« 

o.oi  78 

6 

Ethylene      . 

C2H4C12 

w.yiv^y 
1.2589 

« 

0.0166 

15 

<« 

14 

" 

I.256I 

" 

0.0164 

20 

Jahn. 

Methyl         '.        !        ! 
Methylene  . 
Octyl   .... 

CH8C1 
CH2C12 
C8H17C1 

0.8778 

M 

0.0170 
0.0162 
0.0141 

15 
15 

Becquerel. 
Perkin. 

Phosphorus  protochloride 
Propyl 

PC13 
C3H7C1 

0.8922 

t( 

0.0275 
0.0135 

15 
15 

Becquerel. 
Perkin. 

Silicon 
Sulphur  bichloride      . 

SiCl4 
S2C12 

: 

H 

0.0275 
0.0393 

15 
15 

Becquerel. 

Tin  bichloride 

SnCU 

_ 

H 

0.0151 

1C 

« 

Zinc  bichloride    .        . 

ZnCl2 

- 

• 

0.0437 

•J 

15 

« 

Iodides  : 

Ethyl   

C2H5I 

I  Q4I7 

tt 

0.0296 

Perkin. 

Methyl         .... 

CH3I 

2^2832 

« 

0.0336 

15 

Octyl    

C8Hi7I 

77Q  C 

tt 

O.O2I  7 

Propvl  . 

CsH7I 

?6c8 

M 

O.O27I 

5 

Nitrates  : 

**•**!* 

' 

1^ 

Ethyl  

C2H5O  NO2 

I  I4.Q 

« 

O.OO9I 

Ethylene  (nitroglycol) 

C2H4(N03)2 

.1  iij.y 
.4948 

« 

0.0088 

15 

Methyl 

CH3O.NO2 

•2157 

" 

O.OO78 

15 

Propyl 

C3H7O.N02 

.0622 

« 

0.0  1  00 

15 

Trinitrin  (nitroglycerine) 
Nitro  ethane        .    *  . 

C3H5(N03)3 
C2H6NO2 

•5996 

•°552 

" 

00090 
0.0095 

15 
15 

Nitro  methane    . 

CH3NO2 

.1432 

M 

0.0084 

15 

Nitro  propane 

C3H6NO2 

I.OIOO 

" 

O.OI  O2 

15 

« 

Paraffins  : 

Decane 

CioH22 

0.7218 

« 

0.0128 

23.1 

Schonrock. 

Heptane 

C7H16 

0.6880 

« 

0.0125 

15 

Perkin. 

Hexane 

C6H14 

0.6580 

" 

0.0122 

22.1 

Schonrock. 

... 

u 

0.6743 

" 

O.OI25 

15 

Perkin. 

Octane 

C8Hig 

0.7011 

" 

O.OI28 

23.1 

Schonrock. 

Pentane 

CsHij 

0.6196 

* 

O.OII9 

21.  1 

H 

M 

tt 

0.6332 

* 

O.OIlS 

15 

Perkin. 

Phosphorus  (melted) 
Sulphur  (melted)    . 

P 

S 

« 

0.1316 
0.0803 

33 
114 

Becquerel. 

N 

Toluene 

C7H8 

0.8581 

" 

0.0269 

28.4 

Schonrock. 

... 

" 

- 

" 

0.0243 

15 

Becquerel. 

Water    .... 

H2O 

0.9992 

II 

O*O  I  *?O 

j  r 

H 

M 

0.9983 

« 

0.0131 

18-20 

Quincke. 

** 

tt 

0008  1 

M 

O.O  I  °  2 

2O 

Jahn. 

Xylene  

C  H 

w.yyoj 

(( 

O.O22  1 

T  C 

* 

0.8746 

u 

O.O263 

15 

27 

Schonrock. 

SMITHSONIAN  TABLES. 


TABLE  322. 
MAGNETO-OPTIC  ROTATION. 

Solutions  of  Acids  and  Salts  in  Water. 


301 


Substance. 

Chemical 
formula. 

Density, 
grammes 
per  c.  c. 

Kind 
of 
light. 

Verdet's 
constant 
in  minutes 

Temp. 

V/» 

Authority. 

Acetone   

C3H60 

0.9715 

D 

O.OI29 

20° 

Jahn. 

Acids  : 

Hydrobromic 

HBr 

1.7859 

<« 

0-0343 

15 

Perkin. 

u 

" 

1.6104 

ii 

0.0304 

" 

u 

u 

1-3775 

" 

0.0244 

<« 

« 

« 

1.2039 

«< 

0.0194 

it 

it 

« 

1.1163 

«< 

0.0168 

u 

Hydrochloric 

HC1 

1.2072 

<« 

0.0225 

tt 

n 

n 

1.1856 

M 

0.0219 

II 

« 

M 

i-I573 

M 

0.0204 

" 

u 

« 

1.1279 

M 

0.0193 

«« 

" 

<i 

«« 

1.0762 

M 

0.0168 

« 

«< 

M 

«« 

1-0323 

" 

0.0150 

20 

Jahn. 

M 

(c 

1.0158 

(« 

0.0140 

" 

" 

Hydriodic     .... 

HI 

1-9473 

«« 

0-0513 

«« 

Perkin. 

.        • 

« 

I-9057 

<« 

0.0499 

«« 

<« 

it 

ti 

1.8229 

M 

0.0468 

«< 

« 

N 

1.7007 

<« 

0.0421 

« 

« 

« 

*•/  vyv-f/ 
1-4495 

(( 

0.0323 

« 

M 

<« 

1.2966 

<« 

0.0258 

« 

M 

«< 

1.1760 

(« 

0.0205 

M 

Nitric   

HNOs 

1.5190 

<« 

o.ooio 

«< 

« 

" 

1-3560 

(« 

0.0105 

N 

Sulphuric  -f  3H2O      . 
Ammonia         .... 

H2SO4 
NHS 

0.8918 

«( 
« 

O.OI2I 
0.0153 

«< 
IS 

Becquerel. 
Perkin. 

Bromides  : 

Ammonium  .... 

NH4Br 

1.2805 

«« 

0.0226 

(« 

«« 

« 

M 

1.1576 

H 

0.0186 

M 

<« 

Barium         .... 

« 

BaBr2 
« 

r-5399 
1-2855 

«« 

« 

O.O2I5 
0.0176 

2O 

(« 

Jahn. 

Cadmium      .... 

CdBr2 

1.3291 

«( 

0.0192 

« 

"              .... 

« 

1.1608 

« 

O.OI62 

«( 

Calcium        .        .        . 

CaBr2 

1.2491 

«« 

0.0189 

" 

« 

• 

I-I337 

M 

0.0164 

" 

Potassium     .... 

KBr 

1.1424 

«« 

0.0163 

«( 

« 

« 

1.0876 

«« 

O.OI5I 

« 

Sodium         .... 

NaBr 

I-I35I 

<« 

0.0165 

i« 

M 

« 

1.0824 

" 

O.OI52 

" 

Strontium     .... 

SrBr2 

1.2901 

(« 

0.0186 

(( 

« 

" 

1.1416 

<« 

0.0159 

<« 

Carbonate  of  potassium  . 

K2C08 

1.1906 

(« 

0.0140 

20 

"  sodium 

NaaCOs 

1.  1006 

« 

0.0140 

N 

«           «        « 

H 

1.0564 

M 

0-0137 

(t 

Chlorides  : 

Ammonium  (sal  ammoniac) 

NH4C1 

1.0718 

<« 

0.0178 

15 

Verdet. 

Barium 

BaCl2 

1.2897 

«« 

0.0168 

20 

Jahn. 

" 

" 

I-I338 

H 

0.0149 

" 

«4 

Cadmium 

CdCl2 

r-3!79 

« 

0.0185 

" 

«« 

M 

J-2755 

«« 

0.0179 

«< 

« 

«« 

1.1732 

H 

0.0160 

«« 

(« 

« 

I-I53I 

«« 

0.0157 

" 

«( 

Calcium 

CaCl2 

1.1504 

«« 

0.0165 

M 

H 

"                             .        . 

1.0832 

« 

o.oi  52 

" 

«« 

"                              . 

1.1049 

" 

0.0157 

16 

Schonrock. 

Copper 

CuCl2 

<« 

1.5158 
1.2789 

« 
(« 

O.O22I 

o.o  1  86 

B 

BecquereL 
<« 

« 

«« 

1.1330 

«« 

0.0156 

«« 

« 

SMITHSONIAN  TABLES. 


302 


TABLE  322  (continued). 

MAGNETO-OPTIC    ROTATION. 

Solutions  of  Acids  and  Salts  in  Water. 


Substance. 

Chemical 
formula. 

Density, 
grammes 
per  c.  c. 

Kind 
of 
light. 

Verdet's 
constant 
in  minutes. 

Temp. 

Authority. 

Chlorides  : 

Iron 

FeCl2 

I-433I 

D 

0.0025 

15° 

Becquerel. 

M 

" 

1.2141 

n 

0.0099 

n 

" 

H 

1.1093 

tt 

O.OIlS 

tt 

tt 

.             .                           . 

" 

1.0548 

u 

0.0124 

tt 

u 

(ferric) 

Fe2Cl6 

1.6933 

u 

—  O.2O26 

tt 

" 

. 

w 

I-53I5 

u 

—0.1140 

it 

H 

. 

" 

1.3230 

u 

—0.0348 

* 

tt 

. 

" 

1.1681 

tt 

—  O.OOI5 

u 

tt 

. 

" 

1.0864 

u 

O.OoSl 

tt 

tt 

"       .        . 

u 

1.0445 

tf 

O.OII3 

tt 

ft 

"       .        • 

tt 

1.0232 

ft 

O.OI22 

tt 

ft 

Lithium        .                 . 

LiCl 

1.0619 

tl 

0.0145 

20 

Jahn. 

"              .                 . 

" 

1.0316 

" 

0.0143 

" 

" 

Manganese  . 

MnCl2 

1.1966 

tf 

0.0167 

15 

Becquerel. 

"          .                . 

" 

1.0876 

i( 

o.oi  50 

" 

Mercury 

HgCl2 

1.0381 

* 

0.0137 

16 

Schonrock. 

"              . 

tt 

1.0349 

" 

0.0137 

M 

ti 

Nickel  . 

NiCl2 

1.4685 

tf 

O.O27O 

15 

Becquerel. 

"      . 

" 

.2432 

" 

0.0196 

" 

**      •        . 

" 

•I233 

" 

0.0162 

ft 

" 

" 

tt 

.0690 

ft 

0.0146 

« 

« 

Potassium    . 

KC1 

.6000 

« 

0.0163 

M 

tt 

" 

" 

.0732 

«' 

0.0148 

20 

Jahn. 

««            .                . 

n 

.0418 

it 

O.OI44 

" 

" 

Sodium 

NaCl 

.2051 

ft 

O.OlSo 

15 

Becquerel. 

"             .                . 

" 

.1058 

" 

0.0155 

" 

«             9 

a 

.0546 

" 

0.0144 

« 

" 

tt 

" 

.0817 

u 

0.0154 

20 

Jahn. 

tt 

" 

.0418 

" 

O.OI44 

it 

ft 

Strontium    . 

SrCl2 

1.1921 

" 

0.0102 

ti 

" 

« 

.0877 

" 

0.0146 

tt 

« 

Tin       .        .'                 ! 

SnCl2 

.3280 

" 

O.O266 

15 

Verdet. 

" 

" 

.1637 

" 

0.0198 

"        .        .                 • 

*• 

.1112 

if 

0.0175 

" 

Zinc      . 

ZnCl2 

.2851 

tt 

0.0196 

n 

if 

u 

•I595 

11 

0.0161 

" 

Chromate  of  potassium  . 

K2Cr04 

•359s 

" 

0.0098 

" 

Bichromate  of       " 

K2Cr2O7 

.0786 

" 

0.0126 

tt 

Cyanide  of  mercury 

Hy(CN)2 

.0638 

ft 

0.0136 

16 

Schonrock. 

. 

H 

.0425 

tf 

0.0134 

M 

it        tt        u 

" 

1.0605 

" 

0.0135 

U 

" 

Iodides  : 

Ammonium  . 

NHJ 

.5948 

• 

0.0396 

15 

Perkin. 

it 

" 

.5688 

M 

0.0386 

n 

"                           . 

« 

•5I09 

" 

0.0358 

" 

tt 

.        . 

* 

.2341 

" 

0.0235 

" 

tt 

Cadmium     . 

Cdl 

" 

0.0291 

20 

Jahn. 

"           ... 

tt 

.2770 

" 

0.0215 

" 

M 

tt 

tt 

.1521 

f 

0.0177 

" 

M 

Potassium    . 

KI 

.6743 

" 

0.0338 

«j 

Becquerel. 

"            . 

' 

•3398 

** 

0.0237 

" 

tt 

1 

•1705 

n 

0.0182 

" 

ti 

"           ... 

I 

.0871 

ft 

0.0152 

** 

tt 

"            ... 

• 

.2380 

it 

O.O2II 

2O 

Jahn. 

"            ... 

* 

.1245 

tt 

0.0174 

it 

M 

Sodium 

Nal 

" 

0.0200 

tt 

" 

... 

tt 

.1191 

I 

0.0175 

tt 

tl 

SMITHSONIAN  TABLES. 


TABLES  322  (conttnue<f)-324. 

MAGNETO-OPTIC   ROTATION. 

TABLE  322.  — Solutions  of  Acids  and  Salts  in  Water. 


303 


Substance. 

Chemical 
formula. 

Density, 
grammes 
perc.  c. 

Kind 
of 
light. 

Verdet's 
constant 
in 
minutes. 

TecT 

Authority. 

Nitrates  : 

Ammonium          .        .        . 

NH4NO8 

1.2803 

D 

O.OI2I 

15 

Perkin. 

Potassium    .... 

KNO3 

1.0634 

« 

0.0130 

20 

Jahn. 

Sodium        .... 

NaNO3 

I.III2 

« 

0.0131 

« 

i< 

Uranium      .... 

U2O3.N2O6 

2.0267 

« 

0.0053 

« 

Becquerel. 

.... 

« 

1.7640 

« 

0.0078 

« 

« 

« 

« 

L3865 

« 

0.0105 

M 

(( 

«( 

M 

1.1963 

u 

O.OII5 

(( 

« 

Sulphates  : 

Ammonium 

(NH4)2S04 

1.2286 

(( 

0.0140 

15 

Perkin. 

(acid)        .        . 
Barium        ... 

NH4.HSO4 
BaS04 

I.44I7 
I.I788 

(( 
«( 

0.0085 
0.0134 

U 

20 

(i 

Jahn. 

M 

« 

1.0938 

« 

0.0133 

a 

it 

Cadmium    .... 

CdSO4 

I.I762 

(( 

0.0139 

M 

(1 

• 

" 

1.0890 

(( 

0.0136 

M 

H 

Lithium       .... 

Li2SO4 

I.I762 

« 

0.0137 

« 

M 

Manganese  .... 

MnS04 

1.0942 
I.244I 

(t 
(( 

0.0135 
0.0138 

Ck 

M 

H 
|| 

« 

« 

I.I4I6 

M 

0.0136 

a 

« 

Potassium   .... 

K2SO4 

1.0475 

«( 

0.0133 

tt 

tl 

Sodium        .... 

NaSO4 

1.0661 

M 

0.0135 

u 

H 

TABLE  323.  — Solutions  of  Salts  in  Alcohol. 


Substance. 

Chemical 
formula. 

Density, 
grammes 
per  c.  c. 

Kind 
of 
light. 

Verdet's 
constant 
in 
minutes. 

Temp. 

\*» 

Authority. 

Cadmium  bromide  . 

CdBr2 

1.0446 

D 

o.oi  59 

2O 

Jahn. 

«            « 

<« 

0.9420 

H 

0.0140 

u 

Calcium           " 

CaBr2 

0.9966 

«{ 

0.0154 

M 

"               " 

0.8846 

0.0130 

Strontium       " 

SrBr2 

0.9636 

« 

0.0140 

«( 

«<               «« 

<c 

0.8814 

M 

0.0126 

H 

Cadmium  chloride 

CdCl2 

0.8303 

« 

0.0118 

(( 

Strontium      " 

SrCl2 

0.8313 

tt 

o.oi  18 

H 

«< 

«<              « 

« 

0.8274 

« 

0.0117 

M 

« 

Cadmium  iodide 

CdI2 

1.0988 

H 

0.0199 

« 

« 

M                         <« 

« 

0.9484 

H 

0.0156 

«( 

« 

TABLE  324.—  Solutions  in  Hydrochloric  Acid. 


Substance. 

Chemical 
formula. 

Density, 
grammes 
per  c.  c. 

Kind 
of 
light. 

Verdet's 
constant 
in 
minutes. 

Trap. 

Authority. 

Antimony  trichloride 

SbCls 

2-4755 

D 

0.0603 

15 

Becquerel. 

I-8573 

0.0449 

I-5I95 

0.0347 

1.3420 

0.0277 

Bismuth            " 

Bids 

2.0822 

" 

0.0396 

* 

* 

. 

1-6550 

" 

0.0359 

" 

* 

* 

1.4156 

0.0350 

SMITHSONIAN  TABLES. 


304 


TABLES  325,  326. 
TABLE  325.— Magneto-Optic  Rotation. 
Oases. 


Substance. 

Pressure. 

Temp. 

Verdet's 
constant  in 
minutes. 

Authority. 

Atmospheric  air 
Carbon  dioxide        .... 
Carbon  disulphide  .... 

Atmospheric 

u 

74  cms. 
Atmospheric 

Ordinary 

70°  C. 
Ordinary 

6.83  X  ic-6 

13.00 
23-49 

'JA  A$ 

Becquerel. 

Bichat. 
Becquerel 

Nitrogen          «    ,     « 

u 

« 

« 

« 

6.92 
16.00 

u 

Oxygen   
Sulphur  dioxide      .... 

u                " 

u 

(( 

246  cms. 

« 
a 
20°  C. 

6.28 

31-39  "  . 
38.40  " 

u 

« 
Bichat. 

Du  Bois  discusses  Kundt's  results  and  gives  additional  experiments  on  nickel  and  cobalt. 
He  shows  that  in  the  case  of  substances  like  iron,  nickel,  and  cobalt  which  have  a  variable  mag- 
netic susceptibility  the  expression  in  Verdet's  equation,  which  is  constant  for  substances  of  con- 
stant susceptibility,  requires  to  be  divided  by  the  susceptibility  to  obtain  a  constant.  For  this 
expression  he  proposes  the  name  "  Kundt's  constant."  These  experiments  of  Kundt  and  Du 
Bois  show  that  it  is  not  the  difference  of  magnetic  potential  between  the  two  ends  of  the  medium, 
but  the  product  of  the  length  of  the  medium  and  the  induction  per  unit  area,  which  controls  the 
amount  of  rotation  of  the  beam. 


TABLE  326.  — Verdet's  and  Kundt's  Constants. 


The  following  short  table  is  quoted  from  Du  Bois'  paper.    The  quantities  are  stated  in  c.  g.  s.  measure,  circular 
measure  (radians)  being  used  in  the  expression  of  "  Verdet's  constant  "  and  "  Kundt's  constant." 


Verdet's  constant. 

Name  of  substance. 

Magnetic 
susceptibility. 

Wave-length 
of  light 
in  cms. 

Kundt's 
constant. 

Number. 

Authority. 

Cobalt      . 

_ 

_ 

_ 

6.44  X  io~5 

3-99 

Nickel     . 

_ 

— 

— 

« 

3-iS 

Iron 

4 

— 

— 

6.56       ' 

2.63 

Oxygen  :  I  atmo.     . 
Sulphur  dioxide 

+  O.OI26XIQ-6 

—  0.0751      " 

O.OOOI79X  io~6 
0.302    '       " 

Becquerel. 

14 

5.89       « 

0.014 
—  4.00 

Water      . 

—  0.0694     " 

0-377 

Arons 

—5-4 

Nitric  acid 

-0.0633     * 

0.356 

Becquerel. 

t« 

-5.6 

Alcohol    . 

—  0.0566     " 

0.330 

De  la  Rive. 

-5.8 

Ether.      . 
Arsenic  chloride 
Carbon  disulphide  . 
Faraday's  glass 

—  0.0541      " 
—  0.0876     " 
—  0.0716     " 
—  0.0982     " 

0.315 

1.222                " 
1.222 
1.738 

« 

Becquerel. 
Rayleigh. 
Becquerel. 

« 
M 

H 

-5.8 
—14.9 
—17.1 
—17.7 

SMITHSONIAN  TABLES. 


TABLES  327,  328. 
TABLE  327. -Magnetic  Susceptibility  of  Liquids  and  Oases. 


305 


The  following  table  gives  a  comparison  by  Da  Bois*  of  his  own  and  some  other  determinations  of  the  magnetic  sus- 
ceptibility of  a  few  standard  substances.    Verdet's  and  Kundt's  constants  are  in  radians  for  the  sodium  line  D. 


Substance. 

Verdet's 
constant. 

Faraday's 
value 
£Xio* 

Becquerel's 
value 
*Xio« 

WShner's 
value 
AXio» 

Water  

3.77  X  icr* 

—  0.69 

—0.63 

-0.536 

Alcohol,  C2H6O  . 

3-30       " 

—0-57 

—0.49 

-0.388 

Ether,  C4Hi0O     . 

3-iS       " 

—0.54 

- 

—0.360 

Carbon  disulphicle        .        • 

12.22          " 

—0.72 

—0.84 

—0-465 

Oxygen  at  i  atmosphere 

O.OOI79  " 

0.13 

O.I2 

- 

Air  at  I  atmosphere     . 

0.00194  " 

0.024 

0.025 

- 

Substance. 

Quincke  at  ao°  C. 

Du  Bois  at  15°  C. 

Density. 

/fcXio* 

Density. 

£Xio« 

Kundt's 
constant.. 

Water   

0.9983 

—0.815 

0.9992 

-0.837 

—4.50 

Alcohol,  C2H6O  . 

0.7929 

—0.660 

0.7963 

-0.694 

—4-75 

Ether,  C4Hi0O     . 

0.7152 

—  0.607 

0.7250 

—  0.642 

—4.91 

Carbon  disulphide 

1.2644 

—0.724 

1.2692 

—  0.816 

—14.97 

Oxygen  at  I  atmosphere 

- 

- 

0.00135 

0.117 

0.016 

Air  at  i  atmosphere     . 

- 

- 

O.OOI23 

0.024 

0.08  1 

TABLE  328.— Values  of  Ken's  Constant t 


Du  Bois  has  shown  that  the  rotation  of  the  major  axis  of  vibration  of  radiations  normally  reflected  from  a  magnet  is 
algebraically  equal  to  the  normal  component  of  magnetization  multiplied  into  a  constant  K,  He  calls  this  con- 
stant, K,  Kerr's  constant  for  the  magnetized  substance  forming  the  magnet. 


Color  of  light. 

Spectrum 
line. 

Wave- 
length 
in  cms. 
Xio« 

Kerr's  constant  in  minutes  per  c.  g.  s.  unit  of  magnetization. 

Cobalt 

Nickel. 

Iron. 

Magnetite. 

Red       ... 

Li  a 

67.7 

—  0.0208 

—0.0173 

—0.0154 

+0.0096 

Red       ... 

— 

62.O 

—  0.0198 

—  0.0160 

—0.0138 

+O.OI2O 

Yellow  . 

D 

58-9 

—0.0193 

—0.0154 

—  O.OI3O 

+0.0133 

Green    .        .        . 

b 

51-7 

—  0.0179 

—0.0159 

—  O.OIII 

+0.0072 

Blue      . 

F 

48.6 

—  0.0180 

—0.0163 

—  O.OIOI 

+O.O026 

Violet    . 

G 

43-i 

—  0.0182 

—0.0175 

—0.0089 

- 

*  "  Wied.  Ann."  vol.  35,  P-  163. 
SMITHSONIAN  TABLES. 


t  H.  E.  J.  G.  Du  Bois,  "  Phil.  Mag."  vol.  29. 


306  TABLES  329-331 .    RESISTANCE  OF  METALS. 

TABLE  329.  —Variation  of  Resistance  of  Bismuth,  with  Temperature,  in  a  Transverse  Magnetic  Field. 


Proportional  Values  of  Resistance. 

H 

-193° 

-135° 

-100° 

-37° 

0° 

+18° 

+60° 

+  100° 

+183° 

o 

O.4O 

O.6o 

0.70 

0.88 

1.  00 

1.08 

1.25 

1.42 

1-79 

20OO 

1.16 

0.87 

0.86 

0.96 

1.  08 

I.  II 

1.26 

1.43 

1.  80 

4000 

2.32 

1-35 

1.20 

.10 

I.I8 

I.2I 

1.31 

1.46 

1.82 

6000 

4.00 

2.06 

1.  60 

.29 

1.30 

1.32 

1.39 

1.51 

1.85 

8000 

5.90 

2.88 

2.00 

•50 

1.43 

1.42 

1.46 

1-57 

1.87 

10000 

8.60 

3.80 

2.43 

.72 

1.57 

1.54 

1-54 

1.62 

1.89 

12000 

10.8 

4.76 

2.93 

•94 

I.7I 

1.67 

1.62 

1.67 

1.92 

I4OOO 

12.9 

5.82 

3.50 

2.16 

1.87 

1.  80 

1.70 

1-73 

1-94 

16000 

15.2 

6.95 

4.11 

2.38 

2.02 

1-93 

1.79 

1.  80 

1.96 

18000 

17.5 

8.15 

4.76 

2.60 

2.18 

2.06 

1.88 

1.87 

1.99 

20000 

19.8 

9.50 

5.40 

2.8  1 

2.33 

2.20 

1.97 

1.95 

2.03 

25000 
30000 

25-5 
30.7 

13-3 

18.2 

7.30 

9.8 

3.50 
4.20 

2.73 
3.17 

2.52 

2.86 

2.22 
2.46 

2.10 
2.28 

2.09 
2.17 

35000 

35-5 

20.35 

12.2 

4.95 

3.62 

3-25 

2.69 

245 

2.25 

TABLE  330. -Increase  of  Resistance  of  Nickel  due  to  a  Transverse  Magnetic 
Field,  expressed  as  %  of  Resistance  at  0°  and  H=0. 


H 

—190° 

-75° 

0° 

+18° 

+100° 

+182° 

o 

+0 

0 

o 

O 

o 

O 

IOOO 

+0.20 

+0.23 

+0.07 

+0.07 

+0.96 

+0.04 

2000 

+0.17 

+0.16 

+0.03 

+0.03 

+0.72 

—0.07 

3OOO 

o.oo 

—0.05 

-0.34 

—0.36 

-0.14 

—0.60 

4000 

-0.17 

-0.15 

—0.60 

—0.72 

—0.70 

-I.I5 

6000 

—0.19 

—  0.20 

—0.70 

-0.83 

—  1.02 

8OOO 

—0.19 

-0.23 

—0.76 

—0.90 

-1.  15 

—  1.66 

10000 

-0.18 

-0.27 

-0.82 

-0.95 

-1.23 

-1.76 

I2OOO 

—  0.18 

—0.30 

—0.87 

—  1.  00 

-1.30 

-I.8S 

14000 

-0.18 

-0.32 

—0.91 

-1.04 

-1.37 

-1.  95 

I600O 
18000 

—0.17 
—0.17 

-0.35 
—0.38 

-0.94 
—0.98 

-1.09 
-i.  13 

-1.44 
-1.51 

-2.05 
-2.15 

20000 

—  0.16 

-0.41 

-1.03 

-1.  17 

-1-59 

-2.25 

25OOO 

-0.14 

-0.49 

—  1.  12 

-1.29 

-1.76 

-2.50 

30000 

—0.12 

—0.56 

—  1.22 

-1.40 

-1.95 

-2.73 

35000 

—  O.IO 

—0.63 

-1.32 

-1.50 

-2.13 

-2.98 

F.  C.  Blake,  Ann.  der  Physik,  28,  p.  449;  1909. 


TABLE  331.  -  Change  of  Resistance  of  Various  Metals  in  a  Transverse  Magnetic  Field. 

Room  Temperature. 


Metal. 

Field  Strength 
in  Gausses. 

Per  cent 
Increase. 

Authority. 

Nickel 

IOOOO 

—  1.3 

—  14 

Williams,  Phil.  Mag.  9.  1905. 
Barlow,  Pr.  Roy.  Soc.  71.  1903. 

• 
«• 

6000 
xoooo 

—  I.O 

-14 

Dagostino,  Atti  Ac.  Line.  17.  1908. 
Grummach,  Ann.  der  Phys.  22,  1906. 

Cobalt 

«• 

—0.53 

Cadmium 

" 

+0.03 

Zinc 

'« 

+O.OI 

Copper 

" 

+0.004 

Silver 

M 

+0.004 

Gold 

M 

+0.003 

Tin 

M 

+O.OO2 

Palladium 

« 

+O.OOI 

•• 

Platinum 

" 

+0.0005 

«* 

Lead 

M 

+O.OOO4 

•• 

Tantalum 

M 

+0.0003 

M 

Magnesium 

6000 

+O.OI 

Dagostino,  I.  c. 

Manganin 

•• 

+O.OI 

44 

Tellurium 

? 

+0.02  to  0.34 

Goldhammer,  Wied  Ann.  31,  1887. 

Antimony 
Iron             J 

? 

Different  spec! 
diverse  results, 
crease  in  weak  f 

+0.02  to  0.16 
nens  show  very 
usually  an   in- 
ields.  a  decrease 

Grummach,  {.  c» 
Barlow,  /.  c. 
Williams,  1.  c. 

I 

in  strong. 

Nickel  steel 

Alloys  behave  similarly  to  iron. 

Williams,  1.  c. 

SMITHSONIAN  TABLES. 


TABLES  332,  333.  307 

TABLE  332.  — Transverse  Galvanomagnetic  and  Thennomagnetic  Eifects. 

Effects  are  considered  positive  when,  the  magnetic  field  being  directed  away  from  the  observer, 
and  the  primary  current  of  heat  or  electricity  directed  from  left  to  right,  the  upper  edge  of  the 
specimen  has  the  higher  potential  or  higher  temperature. 

£=  difference  of  potential  produced;  T=  difference  of  temperature  produced;  7=  primary 

current;   ^  =  primary  temperature  gradient;   B  =  breadth,  and  D  =  thickness,  of  specimen; 
H=  intensity  of  field.    C.  G.  S.  units. 


TTT 

Hall  effect  (Galvanomagnetic  difference  of  Potential),  E  =  R-j^ 
Ettingshausen  effect  (  "  " 

Nerast  effect  (Thermomagnetic      "          "  Potential), 

dt 
Leduc  effect  (  "  "  Temperature),  T=  SHB-r- 


TTT 

"  Temperature),  T=P~p- 
dt 


Substance. 

Values  of  R. 

P  X  io«. 

Q  X  io«. 

SXi<*. 

-{-400  to  800 

+  2OO 

—  360000 

-r4°o 

-{-  0.9  "  O.22 

+2 

-{-9000  to  18000 

+  2OO 

Steel          

-f-.OI2  "  0.033 

—  O.O7 

—  700  "  1700 

4-6o 

-j—  OIO  "  O.O26 

-{-1600  "  7000 

-J-.OO7  "  o.on 

—0.06 

—  looo  "  1500 

+39 

Cobalt      

+.0016  "  0.0046 

+0.01 

-j-i8oo  "  2240 

1  J 

-J-I-3 

—  C4   "   240 

••> 

4-i-j 

-J-.OOO?1* 

-f"  .00040 

_ 

up  to  —  5.0 

+5 

Lead    

-r-.OOOOQ 

_ 

—5.0  (?) 

Tin  

—.00003 

_ 

—  4-0  (?) 

—  .0002 

__ 

—  2 

—  .00052 

_ 

—90  to  270 

—  18 

—  .00054 

Gold    

—.00057  to  .00071 

—  .0000 

—  .ooocn 

—  0007  to  .0012 

— 

4-  to  to  no 

—1 

—  .0008  "  .0015 

—  46  "  430 

—  41 

—  .0023 

—  .00094  to  .0035 

—  .00036  "  .0037 

Nickel      

—  .0045   *'  .024 

4-0.04  to  0.19 

4-2OOO  "    9OOO 

—  45 

Carbon     

—  .017 

4-s. 

-4-ioo 

Bismuth                   

'    .. 
—  Up  to  ID. 

•4-7  to  4.0 

—  up  to  132000 

—  200 

TABLE  333.  —Variation  of  Hall  Constant  with  the  Temperature. 


Bismuth.1 

Antimony.* 

H 

—182° 

-90° 

-*3° 

+».5° 

+100° 

H 

—  186° 

-79° 

+«-S° 

4-58° 

1000 

62.2 

28.0 

I7.0 

13-3 

7.28 

17  5< 

3 

0.263 

0.249 

0.217 

2000 

55-° 

25-0 

1  6.0 

I2.7 

7.17 

D 

0.252 

0.243 

O.2II 

3000 
4OOO 

497 
45-8 

22.9 
21-5 

'5-1 
14-3 

I2.I 

"•5 

7.06 
6-95 

6160 

0.245 

02.35 

0.209 

0.203 

5OOO 

42.6 

20.2 

13.6 

II 

.0 

6.8 

\ 

6000 

40.1 

18.9 

12.9 

10.6 

6.72 

Bismuth.8 

H 

+14.5°       +104°         125° 

189° 

2W° 

a3o° 

*59° 

269° 

270° 

890 

5.28             2.57             2.12 

1.42 

1.24 

I.II 

0.97 

0.83 

0.77* 

i  Barlow,  Ann.  der  Phys.  12,  1903.  *  Everdingen,  Comm.  Phys.  Lab.  Leiden,  58. 

*  Traubenberg,  Ann.  der  Phys.  17,  1905.  *  Melting-point. 

Both  tables  taken  from  Jahn,  Jahrbuch  der  RadioactivitSt  und  Electromk,  5,  p.  166;  1908,  who  has  collected  data  Of 
all  observer*  and  gives  extensive  bibliography. 

SMITHSONIAN  TABLES. 


APPENDIX  I. 


TABLES  334,  335. 

THE  SPECIFIC  HEAT  OF  IRON  AT  HIGH  TEM- 
PERATURES. 

Analysis  of  iron  — (o.oi  C,  .02  Si,  .03  S,  .04  P,  trace  Mn). 
TABLE  334.  —  Mean  Specific  Heat  between  0°  and  T°  Centigrade,  So. 


T 

sj 

T 

S0T 

200° 

0.1175 

700° 

0.1487 

250 

.1204 

750 

•1537 

300 

.1233 

800 

.1597 

350 

.1257 

850 

.1647 

400 

.1282 

900 

.1644 

450 

.13" 

950 

.1612 

500 

•1338 

IOOO 

.1557 

550 

.1361 

1050 

.1512 

600 

.1396 

IIOO 

•1534 

650 

.1440 

TABLE  335.  -  Total  Heat  between  0°  and  T°  Centigrade,  <& 


T 

<£ 

Pionchon's  value  recalculated. 

<* 

Barker's  value. 

200 

23-5 

23-5 

300 

36.8 

37-o 

400 

51.6 

Si.3 

500 

66.0 

66.9 

600 

83-2 

83-8 

700 

102.2 

104.1 

800 

I25.O 

127.8 

900 

146.7 

148.0 

IOOO 

166.0 

I5S7 

IIOO 

" 

168.8 

T.  A.  Harker,  Proc.  Physical  Society,  London,  19,  p.  703  ;  1905. 

Pionchon's  data,  based  on  experiments  made  many  years  ago,  should 
be  regarded  only  as  corroborative  of  the  more  recent  and  careful  experi- 
ments of  Harker. 

SMITHSONIAN   TABLES. 


APPENDIX  II. 


DEFINITIONS   OF   UNITS. 

ACTIVITY.     Power  or  rate  of  doing  work;  unit,  the  watt. 

AMPERE.  Unit  of  electrical  current.  The  international  ampere,  "which  is  one  tenth  of  the 
unit  of  current  of  the  C.  G.  S.  system  of  electro- magnetic  units,  and  which  is  represented 
sufficiently  well  for  practical  use  by  the  unvarying  current  which,  when  passed  through 
a  solution  of  nitrate  of  silver  in  water,  and  in  accordance  with  accompanying  specifica- 
tions" (see  pages  xxxiv  and  251),  "deposits  silver  at  the  rate  of  0.001118  of  agrammeper 
second." 

The  ampere  =  i  coulomb  per  second  =  i  volt  through  i  ohm; 

Amperes  =volts/ohms=  wa  tts/  volts  =  (  watts  /ohms)*. 

Amperes  X  volts = amperes 2  X  ohms  =  watts. 

ANGSTROM.     Unit  of  wave-length  =  io~10  metre. 
ATMOSPHERE.     Unit  of  pressure. 

English  normal  =  14.7  pounds  per  sq.  in.  =29.929  in.  =760.18  mm.  Hg.  32°  F. 

French  =760  mm.  of  Hg.  o°  €.=29.922  in.  =  14.70  Ibs.  per  sq.  in. 

BARAD.     C.  G.  S.  unit  of  pressure  =  I  dyne  per  sq.  cm. 
BOUGIE  DECIMALE.     Photometric  standard;  see  page  177. 

BRITISH  THERMAL  UNIT.  Heat  required  to  raise  one  pound  of  water  at  its  temper- 
ature of  maximum  density,  i°  F.  =252  gramme-calories. 

CALORY.  Small  calory = gramme-calory  =  therm  =  quantity  of  heat  required  to  raise  one 
gramme  of  water  at  its  maximum  density,  one  degree  Centigrade. 

Large  calory  =  kilogramme-calory  =  1000  small  calories  =  one  kilogramme  of  water  raised 
one  degree  Centigrade  at  the  temperature  of  maximum  density. 

For  conversion  factors  see  page  227. 
CANDLE.     Photometric  standard,  see  page  177. 
CARAT.     The  diamond  carat  =3.1 68  grains =0.2053  grammes. 

The  gold  carat:  pure  gold  is  24  carats;  a  carat  is  1/24  part. 
CARCEL.     Photometric  standard;  see  page  177. 
CIRCULAR  AREA.     The  square  of  the  diameter  =  i .2733  X true  area. 

True  area  =  0.785398  X circular  area. 

COULOMB.  Unit  of  quantity.  The  international  coulomb  is  the  quantity  of  electricity 
transferred  by  a  current  of  one  international  ampere  in  one  second. 

Coulombs  =  (volts- seconds)  /ohms  =  amperes  X  seconds. 
CUBIT  =  18  inches. 
DAY.     Mean  solar  day  =  1440  minutes  =  86400  seconds  =  1 .0027379  sidereal  day. 

Sidereal  day  =  86164.10  mean  solar  seconds. 
DIGIT.    3/4  inch;  1/12  the  diameter  of  the  sun  or  moon. 

DYNE.  C.  G.  S.  unit  of  force  =  that  force  which  acting  for  one  second  on  one  gramme  pro- 
duces a  velocity  of  one  centimetre  per  second. 

=  weight  in  grammes  divided  by  the  acceleration  of  gravity  in  cm.  per  sec. 
ENERGY.    See  Erg. 
ERG.     C.  G.  S.  unit  of  work  and  energy = one  dyne  acting  through  one  centimetre. 

For  conversion  factors  see  page  227. 

FARAD.  Unit  of  electrical  capacity.  The  international  farad  is  the  capacity  of  a  con- 
denser charged  to  a  potential  of  one  international  volt  by  one  international  coulomb 
of  electricity. 

The  one- millionth  part  of  a  farad  (microfarad)  is  more  commonly  used. 

Farads  =  coulombs/  volts. 
FOOT-POUND.    The  work  which  will  raise  one  pound  one  foot  high. 

For  conversion  factors  see  page  227. 
FOOT-POUND ALS.     The  English  unit  of  work  =  foot-pounds /g. 

For  conversion  factors  see  page  227. 
g.  The  acceleration  produced  by  gravity. 

GAUSS.    A  unit  of  intensity  of  magnetic  field  =  lo8  C.  G.  S.  units. 
GRAMME.    See  page  6. 


3IO  APPENDIX. 

GRAMME-CENTIMETRE.  The  gravitation  unit  of  work=g.  ergs. 
For  further  conversion  factors  see  page  227. 

HEAT  UNIT.    See  Calory. 

HEAT  OF  THE  ELECTRIC  CURRENT  generated  in  a  metallic  circuit  without  self- 
induction  is  proportional  to  the  quantity  of  electricity  which  has  passed  in  coulombs 
multiplied  by  the  fall  of  potential  in  volts,  or  is  equal  to  (coulombs  X volts)  74.181  in 
small  calories. 

The  heat  in  small  or  gramme-calories  per  second  =  (amperes  2X  ohms) /4.i8i=  volts2/ 
(ohms  X 4.181)  =  (volts  X  amperes) /4.i8i  =  watts/4.i8i. 

HEAT.  Absolute  zero  of  heat  =  -273°  Centigrade,  -4594°  Fahrenheit,  -218.4°  Reaumur. 

HEFNER  UNIT.     Photometric  standard;  see  page  177. 

HENRY.  Unit  of  induction.  It  is  "the  induction  in  a  circuit  when  the  electromotive  force 
induced  in  this  circuit  is  one  international  volt,  while  the  inducing  current  varies  at 
the  rate  of  one  ampere  per  second." 

HORSE-POWER.  The  practical  unit  of  power  =  33,000  pounds  raised  one  foot  xper  min- 
ute. 

JOULE.    Unit  of  work  =  io7  ergs. 

Joules  =  (volts2  X  seconds)  /ohms  =  watts  X  seconds = amperes1  X  ohms  X  sec. 
For  conversion  factors  see  page  227. 

JOULE'S  EQUIVALENT.  The  mechanical  equivalent  of  heat  =  4.18 1  XIOT  ergs.  See 
page  227. 

KILODYNE.     looo  dynes.    About  I  gramme. 

LITRE.    See  page  6. 

MEGABAR.     Unit  of  pressure =0.987  atmospheres. 

MEGADYNE.     One  million  dynes.     About  one  kilogramme. 

METRE.    See  page  6. 

METRE  CANDLE.   The  intensity  lumination  due  to  standard  candle  distant  one  metre. 

METRET.  An  exponential  subdivision  of  the  metre.  The  ordinal  number  before  the  word 
metre  denotes  the  power  of  ten  serving  as  the  divisor;  e.  g.,  a  tenth-metret  =  io-10» 
i  /io10  metre.  The  first  metret  is  the  decimetre,  the  second,  the  centimetre,  etc. 

MHO.   The  unit  of  electrical  conductivity.    It  is  the  reciprocal  of  the  ohm. 

MICRO.     A  prefix  indicating  the  millionth  part. 

MICROFARAD.   One  millionth  of  a  farad,  the  ordinary  measure  of  electrostatic  capacity. 

MICRON.     (M)  =one  millionth  of  a  metre. 

MIL.     One  thousandth  of  an  inch. 

MILE.     See  pages  5,  6. 

MILE,  NAUTICAL  or  GEOGRAPHICAL  =  6080.204  feet. 

MILLI-.     A  prefix  denoting  the  thousandth  part. 

MONTH.    The  anomalistic  month  =  time  of  revolution  of  the  moon  from  one  perigee  to 

another  =  27.55460  days. 
The  nodical  month  =draconitic  month  =  time  of  revolution  from  a  node  to  the  same  node 

again  =27. 2 1222  days. 

The  sidereal  month  =  the  time  of  revolution  referred  to  the  stars  =  27.32166  days  (mean 
value),  but  varies  by  about  three  hours  on  account  of  the  eccentricity  of  the  orbit  and 
"perturbations." 

The  synodic  month  =  the  revolution  from  one  new  moon  to  another  =  29. 5306  days  (mean 
value)  =the  ordinary  month.  It  varies  by  about  13  hours. 

OHM.  Unit  of  electrical  resistance.  The  international  ohm  is  based  upon  the  ohm  equal 
to  io9  units  of  resistance  of  the  C.  G.  S.  system  of  electromagnetic  units,  and  "is  repre- 
sented by  the  resistance  offered  to  an  unvarying  electric  current  by  a  column  of  mer- 
cury, at  the  temperature  of  melting  ice,  14.4521  grammes  in  mass,  of  a  constant  cross 
section  and  of  the  length  of  106.3  centimetres." 
International  ohm  =  1.01367  B.  A.  ohms  =  1.06292  Siemens'  ohms. 
B.  A.  ohm  =0.98651  international  ohms. 
Siemens'  ohm =0.94080  international  ohms.     See  page  261. 

PENTANE  CANDLE.     Photometric  standard.     See  page  177. 

PI  =ir  =  ratio  of  the  circumference  of  a  circle  to  the  diameter  =3.14159265359. 

POUNDAL.  The  British  unit  of  force.  The  force  which  will  in  one  second  impart  a  veloc- 
ity of  one  foot  per  second  to  a  mass  of  one  pound. 

RADIAN  =  180° /*•  =  57-29578°  =  57°  i?'  45"  =206625". 

SECOHM.    A  unit  of  self-induction  =  I  second  X  i  ohm. 

THERM  =  small  calory = quantity  of  heat  required  to  warm  one  gramme  of  water  at  its 
temperature  of  maximum  density  one  degree  Centigrade. 

THERMAL  UNIT,  BRITISH  =  the  quantity  of  heat  required  to  warm  one  pound  of  water 
at  its  temperature  of  maximum  density  one  degree  Fahrenheit  =252  gramme-calories, 

VOLT.  The  unit  of  electromotive  force  (E.  M.  F.).  The  international  volt  is  "the 
electromotive  force  that,  steadily  applied  to  a  conductor  whose  resistance  is  one  inter- 
national ohm,  will  produce  a  current  of  one  international  ampere,  and  which  is  repre- 
sented sufficiently  well  for  practical  use  by  1000/1434  of  the  electromotive  force  be- 


APPENDIX.  311 

c 'tween  the  poles  or  electrodes  of  the  voltaic  cell  known  as  Clark's  cell,  at  a  temperature 
of  15°  C  and  prepared  in  the  manner  described  in  the  accompanying  specification." 
See  pages  xxxiv  and  251. 
VOLT-AMPERE.    Equivalent  to  Watt. 

WATT.  The  unit  of  electrical  power  =  io7  units  of  power  in  the  C.  G.  S.  system.  It  is  re- 
presented sufficiently  well  for  practical  use  by  the  work  done  at  the  rate  of  one  Joule 
per  second. 

Watts = volts  X  amperes  =  amperes2  X  ohms  =volts2/ohms. 
For  conversion  factors  see  page  227. 
Watts  X  seconds  =  Joules. 

WEBER.    A  name  formerly  given  to  the  coulomb. 
YEAR.    See  page  108. 

Anomalistic  year  =  365  days,  6  hours,  13  minutes,  48  seconds. 
Sidereal  '    =365     "     6  9        "  9.314  seconds. 

Ordinary          "    =365     "      5       "      48        "         46+ 
Tropical          "    same  as  the  ordinary  year. 


INDEX. 


For  the  definitions  of  units,  see  Appendix. 


PAGE. 

Aberration  constant 109 

Absorption  of  gases  by  liquids 141 

Absorption  of  light:  atmospheric 179 

color  screens 195 

Jena  glasses  ......  193 

various  crystals      .     .     .     .194 

Acceleration  of  gravity 104-107 

Aerodynamic  data:  soaring  data 123 

wind  pressures 122 

Agonic  line US 

Air:  density 160 

Air  thermometer,  comparisons 234 

Air:  transmissibility  of,  for  radiation    .     .     .     .179 

Alcohol:  density 98-100 

vapor  pressure 146 

viscosity 126 

Alloys:  densities 89 

electrical  conductivity  of .     .     .     .     266-268 

resistance  of       ....    262-268 

.  low  temp.  .    .    .  264 

melting-points 214 

specific  heats 230 

thermal  conductivity 199 

thermoelectric  powers 258-259 

Alternating  currents,  resistance  of  wires  for   .     .  269 

Aluminum  wire,  weights  of 64 

Alums:  indices  of  refraction 181 

Antilogarithms 26-28 

Aqueous  solutions :  boiling-points 219 

densities 92 

alcohols 98 

alcohol,  temperature  var'n  100 

diffusion  of 136 

electrolytic  conductivities  272-278 

Aqueous  vapor:  vapor  pressure,  low  temp  .   .       151 

o°  to  100°  C         152 

100°  to  230°  C      153 

pressure  of,  in  atmosphere     .        155 

(saturated)  weight  of  ...        154 

Astronomical  data 108-109 

Atmosphere,  aqueous  vapor  in 155 

transmissibility  for  radiation  .     .     .179 
Atomic  weights 270 

Barometer:  boiling  temperature  of  water  for  va- 
rious heights 168-169 

correction  for  capillarity      .     .     .     .121 

latitude,  inch     .     .     .119 

metric      .     .120 

sea  level 118 

temperature .     .     .     .117 

heights,  determination  of,  by  ...  167 

Batteries:  composition,  electromotive  forces  .     .252 

Beaume  scale:  conversion  to  densities    ....     84 

Birmingham  wire  gauge 59 

Bismuth,  resistance  of,  in  magnetic  field      .     .     .  306 

"Black-body"  radiation 238 

Boiling-points:  chemical  elements 210 

inorganic  compounds     .     .     .     .213 

organic  compounds 215 

Boiling-p\>int,  raising  of,  by  salts  in  solution  .     .219 

of  water  and  barometric  pressure  .  168 

Brass  wire,  weights  of,  common  measure  ...    60 

metric  measure      ...    62 

Brick,  crushing  strength  of 71 

British  wire  gauge 59 

British  weights  and  measures 7-10 

Cadmium  line,  wave-length  red 170 

Candle  power,  standard 177 

Capacity,  specific  inductive:  crystals     ....  284 

gases 279 

liquids       ....  280 
liquid  gases   .    .    .282 


PAGE. 

Capacity,  specific  inductive:  solids 283 

Capillarity,  correction  to  barometer  for     .     .     .121 

liquids 142-143 

liquids  near  solidifying  point  .     .     .143 
salt  solutions  in  water     .     .     .     .   \  142 

thickness  of  soap  films 143 

Carcel  unit 17? 

Cells,  voltaic:  composition,  E.  M.  F.     .     .     252-253 

double-fluid 253 

secondary 253 

single-fluid 252 

standard 251,  253 

storage 253 

Chemical,  electro-,  equivalents 270 

equivalent  of  silver .     .     .     .251 

Chemical  elements:  atomic  weights 270 

boiling-points 210 

compressibility 76 

conductivity,  thermal .     .     .199 

densities 85,  9i 

electro-chemical  equivalents    270 

hardness 76 

melting-points 209 

resistance,  electrical    .     262-263 

specific  heats 228 

thermal  conductivities     .     .  199 
expansion,  linear     .  222 

Circular  functions:  argument  (0/) 30 

(radians)  ....    35 

Coals,  heat  of  combustion  of 202 

Cobalt,  magnetic  properties  of     ......  293 

Color  screens 195-196 

Combination,  heat  of 204 

Combustion,  heat  of:  coals 202 

explosives 203 

fuels  (liquid) 202 

peats 202 

Compressibility:  chemical  elements      ....    76 

gases 79-81 

liquids 82 

solids 83 

Concretes:  resistance  to  crushing 71 

Conductivity,  electrical:  see  Resistance. 

alloys 266-268 

alternating  currents,  effect  of     .  269 
magnetic  field,  effect  of     ...  306 

electrolytic 272-278 

equivalent     .     ,     .     275-278 

ionic  (separate  ions)   .     .278 

specific  molecular  .     .     .  273 

limiting  values  274 

temp'ture  coef.  274 

glass  and  porcTn,  temp'ture  coef.  285 

Conductivity,  thermal:  gases 200 

liquids 200 

salt  solutions    .     .     .     .200 

solids 199 

water 200 

Contact  differences  of  potential    ....     254-256 

Convection,  cooling  by 239-240 

Conversion:  Beaume  to  specific  gravities  ...     84 

factors  for  work  units 227 

Cooling  by  radiation,  perfect  radiator  ....  238 
and  convection    .     .     230-240 

Cosines,  hyperbolic  natural 41 

logarithmic 42 

Critical  data  for  gases 221 

Crushing,  resistance  to:  bricks 71 

concretes 71 

stones 71 

timber,  wood  ....    72 

Cubical  thermal  expansion:  gases 226 

liquids 225 

solids 224 


314 


INDEX. 


Crystals:  dielectric  constant 284 

elasticity 77-78 

expansion,  cubical  thermal      .     .     .     .224 
transmissibili ty  for  radiation  .     .     .     .194 

Current,  absolute,  measures 251 

Cyclic  magnetization,  energy  losses  in  .     .     294-296 

Declination,  secular  change  of  magnetic    .     .     .no 

Demagnetizing  factors  for  rods 289 

Density  :  air  :  values  of  h/76o 160 

alcohol :  aqueous  ethyl 98 

methyl 98 

temperature  variation  .    .    .100 

alloys 89 

aqueous  alcohol    . 98 

salt,  acid,  basic  solutions   .     .     92 

chemical  elements 85,  91 

earth 108 

gases 91 

liquids 90 

mercury 97 

metals 85 

organic  compounds 215 

water 95-96 

woods 87 

Dew  points 156 

Dielectric  constant:   (specific  inductive  capacity) 

calibration,  standards  for  .  283 

gases,  atm.  pressure      .     .  279 

pressure  coef .       .     .  279 

temperature  coef.     .  280 

liquids 280 

temperature  coef.     .  282 

solids 283 

Dielectric  strength:  air:  alternating  potential     .  248 
steady  potential  .     .     .  248 

kerosene 250 

large  spark-gaps  .     .     .  249 
pressure  effect      .     .     .  249 
various  materials      .    .250 
Difference  of  potential: 

cells:  double  fluid 253 

secondary 253 

single  fluid 252 

standard 251,  253 

storage 253 

contact:  liquids-liquids  in  air  .  254 
metals  in  salt  solutions  257 
salts  with  liquids  .  .  254 
solids-solids  in  air  .  .256 

thermo-electric 258 

platinum  couples  259 

Differential  formulae 12 

Diffusion:  aqueous  solutions,  water 136 

gases  and  vapors  :  coefficients   .     .     .138 

metals  into  metals 138 

vapors 137 

Diffusion  integral 50 

Dip,  magnetic 112 

secular  change 112 

Dynamical  equivalent  of  thermal  unit  .    .    .    .227 

e,  value  of ia 

e*,  e~*,  and  their  logarithms 43.  47 

log.  f,  x  from  10  to  30 44 

e**,e-**,  and  their  logarithms 45 

£**.  fT**,  and  their  logarithms 46 

e^~°,  £"**'*,  and  their  logarithms   ....    46 


,  and  their  logarithms 41,  42 


2 

e*-e 


39,40 

Earth :  densities 108 

miscellaneous  data 108 

Elasticity:  crystals    . 77, 78 

moduli  of  rigidity 74 

modulus,  Young's 75 

Electrical  conductivity:  alloys     ....     266-268 
alternating  current,  effect  of  269 
magnetic  field,  effect  of    .    s  306 
Electrical  resistance:  see  Conductivity. 

metals  and  alloys,  low  temp.  264 
ohm,  various  determinations  261 
specific:  metallic  wires  .  .  262 

metals 263 

temperature  effect,  glass       .  285 


Electricity,  specific  heat  of 258 

Electric  units,  dimensional  formulae xxvi 

Electrochemical  equivalents 270,  273 

silver 351 

Electrolytic  conductivity: 272-278 

dilute  solutions 272 

equivalent  j  .    .    .    .    375-278 

ionic 278 

specific  molecular  ....  273 
limiting  values  274 
temp.  coef.  .  274 

Electromagnetic  system  of  units xxix 

Electromagnetic/electrostatic  units  —  v      .  247 

Electromotive  force:  cells:  double  fluid      .  253 

secondary     .     .  253 

single  fluid   .     .  252 

standard  .     .     .    251   253 

storage     .     .     .  253 

liquids-liquids  in  air  254 

metals  in  salt  solutions          257 

salts  with  liquids  .     .  254 

solids-solids  in  air      .  256 

thermo-electric      .     .  258 

(platinum)     259 

Elements:  atomic  weights   ........  270 

boiling-points 210 

compressibility 76 

conductivity,  thermal 199 

densities 85, 91 

electrochemical  equivalents  .     .     .     .270 

hardness 76 

melting-points 209 

resistance,  electrical 263 

specific  heats 228 

spectra  (prominent  lines)       .     .     .     .170 

thermal  conductivities 199 

expansion,  linear      .     .     .     .222 
cubical,  gases  .     .  226 

Elliptic  integrals 57 

Emission  of  perfect  radiator 238 

Equivalent,  electro-chemical:  elements      .     .     .270 

ionic 272 

silver 251 

Equivalent,  mechanical,  of  heat 227 

Energy,  data  relating  to  solar 179 

Ethyl  alcohol,  specific  gravity  of  aqueous  ...    98 

Ettinghausen  effect 307 

Expansion,  thermal:  cubical,  crystals    .     .     .     .224 

gases 226 

liquids       ....  225 

solids 224" 

linear,  elements     ....  222 

various 223 

perfect  gas 162 

Explosives,  composition,  etc 203 

Exponential  functions:  «*,  «"*,  their  logs.  .  .  43,  47 
log.  e*.  *=  10  to  30  .  .  44 
«*a,  e-**,  their  logs  .  .  .  45 

€**,  €~**  "     "...    46 


,  their  logs.    46 


their  logs.  .     .   41, 


-*  i    — 


diffusion  integral    .     .         50 

hyperbolic  sines     .     .         39 

cosines       .          41 

logs,  hyperbolic  sines  40 

cosines       42 

probability  integral    .   47,  48 
Eye,  sensitiveness  of,  to  radiation     .....  178 

Fabry-Buisson,  standard  arc  Fe  wave-lengths    .  170 
Factorials,  n  !     ............     38 

Fechner's  law    ...........     .'  178 

Field:  earth's  magnetic  field,  components  of    110-115 

magnetic,  behavior  of  metals  in  .     .     286-296 

resistance  of  metals  in     .....  306 

rotation  of  plane  of  polarization  297-304 

thermo-,  galvanometric  effects     .     .  307 

Films,  thin:  thickness,  colors,  tension  of      .     142,  143 

Fluorite:  index  of  refraction      .......  184 

Formulae,  conversion:  dynamic  units     ....      a 

electric       "    .     .....      3 

fundamental  .....      a 

geometric  ......      a 


INDEX. 


315 


formula,  conversion:  heat 3 

magnetic 3 

see  INTRODUCTION. 

Frautihofer  lines,  wave-lengths  of 176 

Freezing  mixtures 220 

Freezing-points,  lowering  of,  by  salts  in  solution    217 

Friction,  coefficients  of 124 

Fuels,  heats  of  combustion  of        202 

Functions:  circular  arguments  (°  ') 30 

(radians)      ...    35 

exponential 39~47 

gamma 52,  38 

hyperbolic 30-42 

Fundamental  units 2 

Fusion,  latent  heat  of 208 

Galvanometric  effects  of  magnetic  field      .     .     .  307 

Gamma  function 52,  38 

Gaaes:  absorption  of,  by  liquids  ....     140,  141 

atomic  weights 270 

compressibility  of 79-8i 

conductivity,  thermal 200 

critical  data  for 221 

densities 91 

dielectric  constants  . 279,  280 

diffusion 138 

expansion  of  perfect 162 

expansion,  thermal 226 

heat,  conductivity  for 200 

indices  of  refraction 190 

magnetic  susceptibility 305 

magneto-optic  rotation 304 

refractive  indices  of 190 

sound,  velocity  of,  in 102 

solubility  of 140,  141 

specific  heats 732 

thermal  conductivity 200 

thermal  expansion 226 

viscosity  of 134 

volume  of  perfect  (1+0.003760  .     .     162-166 

Gas  thermometry 233-235 

Gauges,  wire:  Birmingham 59 

British  standard 59 

Blown  and  Sharp 66 

Geodetic  data 108 

Geometric  units,  conversion  factors  for      ...       2 

Glass:  indices  of  refraction 180 

:     transmissibility  of  Jena 193 

various      .     .     .     195-196 
electric  resistance,  temp,  variation      .     .  285 

Glass  vessels,  volumes  of n 

Gravity,  force  of 104-106 

correction  to  barometer 118 

Gyration,  radii  of       58 

Hall  effect 307 

Hardness 76 

Harmonics,  zonal 54 

Heat:  combination,  heat  of 204 

combustion:   coals 202 

explosives 203 

fuels  liquid 202 

peats     .     .     .     .     .     .     .     .  202 

conductivity  for:  gases 200 

liquids 200 

salt  solutions    ....  200 

solids 199 

water 200 

latent  heat  of  fusion       208 

vaporization ....     206,  241 

mechanical  equivalent  of 227 

specific:  elements 228 

gases 232 

liquids 230 

mercury       229 

minerals 231 

rocks 231 

solids 230 

vapors 232. 

water 229 

"Heat,  specific,"  of  electricity 258 

Hefner  photometric  unit 177 

Heights  determinations  of  by  barometer    .     .     .167 

Horizontal  intensity  of  earth's  field       .     .     .     .114 

secular  change  114 

Humidity,  relative 158 

Humidity  term,  0.378* 159 

Hydrogen  thermometer 233 

Hyperbolic  cosines,  natural 41 

logarithmic 42 

Hyperbolic  shies,  natural 39 

logarithmic 40 


Hysteresis:  soft  iron  cable  transformer  ....  294 

wire 294 

steel,  transformer       296 

various  substances 295 

Iceland  spar,  refractive  index  of 184 

Inclination  (dip)  of  magnetic  needle      .     .     .     .  na 

secular  change  of 112 

Index  of  refraction:  alums 181 

crystals 187 

fluorite 184 

gases  and  vapors  ....  190 

glass 180 

Iceland  spar 184 

liquids 189 

metals,  metallic  oxides  .  .182 
monorefringent  solids  .  .186 
nitroso-dimethyl-aniline  .  184 

quartz 185 

rock-salt 183 

salt  solutions 188 

silvine 186 

solids,  isptropic     ....  186 

Inductance,  table  for  computing  mutual    ...    56 

Inductive  capacity,  specific:  calibration  st'ds     .  283 

gases,  atm.  pressure    279 

pressure  coef.  279 

temp.  coef.    .  280 

liquids 280 

temp.  coef.    .  282 

solids 283 

Inertia,  table  of  moments  of 58 

Inorganic  compounds:  boiling-points    .     .     .     .213 
melting-points        .     .     .211 

Integral,  diffusion 50 

elliptic 57 

gamma  function 52 

probability 45.  47~48 

Integrals,  elementary 12 

Intensity,  horizontal,  of  earth's  field      .     .     .     .113 
secular  variation  113 

total,  of  earth's  field 114 

secular  variation    114     N 

lonization  of  water 278 

Ions:  equivalent  conductivity  of 278 

Iron:  hysteresis  in  soft        294 

magnetic  properties  of,  weak  fields  .     .     .  294 
saturated     .     .     .  293 

permeabilities 286-292 

specific  heat  at  high  temperatures    .     .     .  308 

standard  arc  lines,  Fabry-Buisson     .     .     .  170 

Kayser 174 

Joule's  (mechanical)  equivalent  of  heat     .     .     .  227 

Kayser's  standard  iron  arc  spectrum     ....  174 
Kerosene,  dielectric  strength    ........  250 

Kerr's  constant ."305 

Kundt's  constant 304 

definition  of 304 

Latent  heat  of  fusion 208 

vaporization 206, 241 

Latitude  correction  to  barometer  ....     110-120 

Least  squares 47~49 

Legal  electrical  units xxxiv 

Leduc  thermomagnetic  effect 307 

Light:  indices  of  refraction 181-190 

reflection  of;  function  of  "n"     .     .     .     .191 

metals 192 

sensitiveness  of  eye  to 178 

transmissibility  to,  of  substances     .     193-196 

polarized:  rotation  of  plane  by  solutions     197 

rotation,  magneto  •    .     .     297-304 

wave-lengths:  cadmium  st'd  line   .     .        170 

elements,  brighter  lines        170 

Fraunhofer,  lines      .  176 

st'd  iron  arc,  Fabry  170 

Kayser  174 

solar,  Rowland  171 

velocity  of 109 

Linear  thermal  expansion  coef.  of  elements  222 

various      .  223 

Liquids:  absorption  of  gases  by 141 

capillarity  of 142-143 

compressibility  of 82-83 

conductivity,  thermal 200 

densities 85,  90,  95-96 

dielectric  constants 280-282 

dielectric  strength 250 

diffusion,  aqueous  solutions    ....  136 
i,  thermal 225 


INDEX. 


Liquids :  fuels,  heat  of  combustion 202 

magnetic  susceptibility 305 

magneto-optic  rotation 304 

potential  differences  with  liquids  .  .  254 
metals  .  .25? 
salts  .  .  .  254 

specific  heats 230 

surface  tensions 142-143 

thermal  conductivity 200 

expansion 225 

vapor  pressures 144-153 

velocity  of  sound 102 

viscosity 127-128 

Logarithms 24 

1000-2000 22 

anti- 26 

.9000-1.0000 28 

Lowering  of  freezing-points  by  salts 217 

Maclaurin's  theorem 12 

Magnetic  field:  bismuth,  resistance  in  ....  306 
Ettingshausen  effect  ....  307 
galvanomagnetic  effects  .  .  .  307 

Hall  effect 307 

Leduc  effect 307 

Nernst  effect 307 

nickel,  resistance  in      ....  306 

optical  rotation  ....     297-304 

resistance  of  metals  in      ...  300 

thermo-magnetic  effects    .     .     .  307 

Magnetic  properties:  of  cobalt  at  100°  C  .    .     .  293 

iron:  hysteresis    .     294-296 

permeability 

286-288.  292-293 
saturated  .  .  .  293 
weak  fields  .  .  294 

magnetite 293 

nickel  at  100°  C  .     .     .  293 

Magnetic  susceptibility,  liquids,  gases  ....  305 
Magnetic  units,  conversion  formulae      ....      3 

Magnetism,  terrestrial:  agonic  line 115 

declination no 

dip 112 

horizontal  intensity    .     .113 

inclination 112 

intensity,  horizontal  .     .113 
total .     .     .     .114 

Magneto-optic  rotation 297-304 

Masses  of  the  earth  and  planets 109 

alloys 89 

elements,  liquid  and  solid 85 

solids 88 

woods 87 

Materials,  strength  of :  bricks 71 

concrete 71 

metals 71 

stones 71 

timber 72-73 

woods 72-73 

Mechanical  equivalent  of  heat 227 

Melting-points:  chemical  elements 209 

inorganic  compounds   .     .     .     .211 

mixtures  (alloys) 214 

(low  melting-points)    .214 
organic  compounds       .     .     .     .215 

Mercury:  density  of       97 

electric  resistance  of     ....     262-263 
pressure  of  columns  of      .     .     .     .     .116 

specific  heat 229 

vapor  pressure 148 

Metals  :  diffusion  of,  into  metals 138 

indices  of  refraction 182 

potential  differences  with  solids    .     .     .256 
solutions  .     .  257 

reflection  of  light  by 192 

refractive  indices 182 

resistance,  electrical 262-263 

specific 263 

sheet,  weight  of 70 

Metallic  oxides,  refractive  indices 182 

Methyl  alcohol,  density  of  aqueous 98 

Metric  weights  and  measures:  British  equiv  .      7-10 
U.  S.  equivalents  5-6 

Minerals,  specific  heats  of 231 

Mixtures,  freezing 220 

Moduli  of  elasticity:  rigidity 74 

'Young's 75 

Molecular  conductivities:  equivalent    .     .     275-278 
specific     .     .     .     271-274 

Moments  of  inertia S8 

Musical  scales 103 

Mutual  inductance,  table  for  computing   ...    56 


Nernst  thermo-magnetic  difference  of  potential  .  307 
Neutral  points,  thermo-electric     ....     258-259 

Newton's  rings  and  scale  of  colors 198 

Nickel:  Kerr's  constants  for 305 

magnetic  properties  of,  at  100°  C  .     .     .  293 

resistance  in  magnetic  field       ....  306 

Nitroso-dimethyl-aniline,  refractive  index      .    .184 

Ohm,  various  determinations  of 261 

legal  value 261 

Oils,  viscosity  of 126 

Organic  compounds,  boiling-points 215 

densities 215 

melting-points       .     .     .     .211 

Parallax:  solar;  lunar 109 

Peltier  effect 258,  260 

Pendulum,  length  of  seconds 107 

Perfect  gas,  expansion  of 162 

volume  of 162 

Permeabilities,  magnetic      .     .     .    286-288,  292-293 

Photometric  standards 177 

Pi,  IT,  value  of 12 

Planck's  radiation  formula 238 

Plane,  data  for  the  soaring  of  a 123 

Planets,  miscellaneous  data 109 

Poisson's  ratio 76 

Polarized  light:  by  reflection 191 

rotation  by  magnetic  field     297-304 
solutions        .     .        197 
Potential  difference:  cells:  double  fluid 
secondary 
single  fluid 
standard  . 
storage     .     .     . 
contact:  liquid-liquid 
liquid-salt    . 
metal-liquid 
solid-solid    . 
sparking:  air    ... 
kerosene    . 


251 


various 
thermoelectric  . 


253 
253 

252 
253 
253 
254 
254 
257 
256 

248-249 
250 
250 

258-259 
.  .  109 

Pressure:  barometric  measures      ....     117-121 
barometric  and  boiling  water  .     .     168-169 

heights 167 

mercury  columns,  due  to 116 

water  columns,  " 116 

wind 122 

Pressure,  vapor:  alcohol,  ethyl  and  methyl  146 

aqueous  :  low  temperature          151 

o°  to  100°  C    .  152 

100°  to  230°  C  153 

in  atmosphere  155 

mercury 148 

salt  solutions 149 

various     ......     144-148 

Probability  tables 47-48 

Purkinje's  phenomenon .  178 

Quartz  fibres,  strength  of 71 

refractiw  index  of 185 

Radiation:  black-body 238 

constants  of 238 

cooling  by,  and  convection  .     .     239-240 

eye,  sensitiveness  of,  to 178 

Planck's  formula 238 

sensitiveness  of  the  eye  to  ....  178 

"solar  constant"  of 179 

Stefan's  formula 238 

transmissibility  of  atmosphere  to      .  179 

Radii  of  gyration 58 

Refraction,  indices  of:  alums 181 

crystals 187 

fluorite 184 

gases  and  vapors    .     .     .190 

glass 180 

Iceland  spar ^184 

liquids 189 

metals,  metallic  oxides  .  182 
monorefringent  solids  .  186 
nitroso-dimethyl-aniline .  184 

quartz 185 

rock-salt 183 

salt  solutions     .     .     .     .188 

silvine 183 

solids,  isotropic       .     .     .  186 
Reflection  of  light:  by  metals  .     .     .     .     .    .  '.  192 

terms  of  "  n  "  and   V     .191 
Relative  humidity IS8 


INDEX. 


317 


Resistance:  see  also  Conductivity. 

alloys,  low  temperature  ....  264 
alternating  current,  effect  of  ...  269 
electrolytic,  see  Conductivity. 

glass  and  porcelain 285 

legal  unit  of 261 

magnetic  field,  of  bismuth  in   ...  306 

metals  in      ...  306 

nickel  in  ....  306 

metals  at  low  temperatures     .     .     .  264 

ohm,  various  determinations  of    .     .261 

specific:  metals 263 

wires 262 

temperature  variation     .     .  262-266,  285 

wire  (copper)  table,  common  units  .    66 

metric  units .     .    68 

Rigidity,  modulus  of 74 

temperature  variation    .     .    74 

Ring  correction  (magnetization)        288 

Rock-salt,  indices  of  refraction 183 

Rods,  demagnetizing  factors  for 289 

Rotation  of  polarized  light:  by  solutions    ,    .     .19? 

Rotation,  magneto-optic:  formulae 297 

gases        304 

Kerr's  constant     .     .  305 

liquids 299 

solids 298 

solutions  .     .     .     301-303 

Verdet's  constant  297-304 

Rowland's  standard  wave-lengths 171 

Salts,  lowering  of  freezing-point  by 217 

raising      "  boiling-     '         " 219 

Saturation,  magnetic,  for  steel 293 

Scales,  musical 103 

Screens,  color 195-196 

Seconds  pendulum 107 

Secondary  batteries 253 

Sections  of  wires 59-66 

Shearing  tests  of  timber 72-73 

Sheet  metal,  weights  of 70 

Silver,  electro-chemical  equivalent    .     .     .    251,  270 

Silvine,  indices  of  refraction 183 

Sines,  natural  and  logarithmic,  circular      .     .   30-38 
hyperbolic     .    39-40 

Sky-light,  comparison  with  sunlight 179 

Soaring  of  planes,  data  for 123 

Solar  constant  of  radiation 179 

energy,  data  of 179 

wave-lengths,  Rowland's     .     .     .     .     .     .171 

Solids:  compressibility 76,  83 

densities 85-89 

dielectric  constant 283 

electrical  resistance 261-269 

hardness 76 

indices  of  refraction 183-187 

magneto-optic  rotation  by 298 

thermal  conductivity .  199 

expansion 222-224 

Solutions:  boiling-point,  raising  by  salts  in     .     .  219 
boiling-points  of  aqueous      .     .     .     .219 

conductivity,  thermal 200 

electrolytic       .     .     272-278 

densities  of  aqueous 92-93 

diffusion  of  aqueous 136 

freezing-points,  lowering  by  salt     .     .217 
of  aqueous    .     .     .     .217 

indices  of  refraction 188 

magneto-optic  rotation  of  .  .  301-303 
potential  (contact)  differences  .  254-257 
specific  heats  .......  230-231 

surface  tensions 142 

viscosities 129-133 

Sound,  velocity  of,  in  solids 101 

liquids  and  gases      .     .     .102 

Sparking  potentials 248-250 

Specific  gravity,  see  Density. 

heat  of  air 232 

elements 228 

gases 232 

iron  at  high  temperatures     .     .  308 

liquids 230 

mercury 229 

minerals  and  rocks 231 

solids     .     .   f. 230 

vapors  . 232 

water 229 

"  Specific  heat  of  electricity  " 258 

Specific  inductive  capacity:  gases      .    .    .     279-280 
liquids    .     .     .     280-282 

solids 283 

Specific  molecular  conductivities  ....     373-274 


Specific  resistance 262-263 

viscosity:  gases  and  vapora  .    .    .     134-135 
liquids  and  oils     .     .    .     126-128 

solutions 129-133 

•Spectra:  elements,  brighter  lines 170 

iron,  Fabry-Buisson 170 

Kayser 174 

solar,  Fraunhofer  lines 176 

Rowland's  measures       .     .     .     .171 

Squares,  least,  tables       47~49 

Standard  cells 251-253 

wave-lengths:  Fabry-Buisson      .     .     .  170 

Kayser 174 

Rowland 171 

Standards,  photometric 177 

Steam  tables:  metric  units       241 

common  " 242 

Steel:  magnetic  properties:  hysteresis     291,  294-296 

permeabilities      286-294 

Stefan- Boltzmann  radiation  formula     ....  238 

Stone:  strength  of 71 

thermal  conductivity 199 

Storage  batteries 253 

Strength  of  materials:  bricka 71 

concrete 71 

metals 71 

stones 71 

timber,  woods     .     .     .    72-73 

Sun:  constant  of  radiation 179 

disk;  distribution  of  intensity      .     .     .     .179 

light;  ratio  to  sky-light 179 

parallax 109 

radiation 179 

spectrum 171,  i?9 

temperature 179 

Surface  tension 142-143 

Susceptibility,  magnetic,  liquids  and  gases     .    .  305 
Sylvine,  refractive  indices .183 

Taylor's  series        12 

Temperature,  critical,  for  gases 221 

resistances  for  low 264 

sun's 179 

Tensile  strengths 71-73 

Tension,  surface 142-143 

vapor,  see  Vapor  pressure. 

Terrestrial  magnetism:  agonic  line 115 

declination,  secular  change    no 

dip 112 

secular  change      .     .     .112 

horizontal  intensity    .     .     .113 

secular  change  113 

inclination 112 

secular  change   .  112 

total  intensity 114 

secular  change  114 

Thermal  conductivities:  gases 200 

liquids 200 

salt  solutions    ....  200 

solids 199 

water 200 

Thermal  expansion:  cubical:  crystals         .         .224 

gases  .         .226 

liquids  .          .  225 

solids  .         .  224 

linear:  elements         .         .  222 

various  .          .  223 

Thermal  unit,  dynamical  equivalent  .         .  227 

Thermo-electricity 258-260 

Peltier  effect     ....    258,  260 

Thermo-magnetic  effects 307 

Thermometer:  air-i6,  o*  to  300°  C 234 

59,  100°  to  200°  C    .     .     .     .  234 

high-temperature-59      .     .     .  235 

hydrogen- 1 6,  o°  to  100°  C  .    .    .  233 

16,  59,  -5°  to  -35°  C    .  233 

59,  o°  to  100°  C  .     .    .  233 

various 235 

Thermometer  stem  correction 236-237 

Thomson  thermo-electric  effect 258 

Timber,  strength  of 72-73 

Time,  sidereal,  solar 108 

Transformer-iron,  permeability  of     ...     286-287 

steels,  energy  losses  in  ...     294  296 

Transmissibility  to  radiation:  atmospheric     .        179 

crystals  ...        194 

glass  ....        193 

Trigonometric  functions:  arguments  (°  0    .    .         30 

(radians)          35 

United  States  weights  and  measures,  conversion 
to  metric  units 5-0 


INDEX. 


Units  of  measurement:  definitions,  see  APPENDIX. 

conversion  factors     ....  2-3 
discussion,  see  INTRODUCTION. 

photometric 177 

ratio  of  electro-magnetic  to  static      .     .     .  247 

V,  ratio  of  electro-magnetic  to  -static  units 

Vapor,  aqueous:  vapor  pressure,  low  temp. 

o°-ioo°  C 

I00°-230°  C 

pressure  of,  In  atmosphere 
relative  humidity  .     .     . 
(saturated)  weight  of  .     . 

Vaporization,  latent  heat  of 

for  steam   .    .241 

Vapors:  densities , 

diffusion  of 137 

indices  of  refraction 

pressures:  alcohol,  ethyl,  methyl  .     .     , 

aqueous:   low  temp.      .     .     . 

o°-ioo°  C      .     .     . 

I00°-230°  C  .      .      . 

mercury 

salt  solutions 

various 144 

specific  heats 

viscosity,  specific    .     .     . 

Velocity  of  light 

sound;  in  gases  and  liquids 

solids     ..... 
Verdet 's  constants:  Verdet  and  Kundt's    . 

gasesj 304 

liquids 295 

solids 

solutions,  alcoholic  .     . 
aqueous  .     . 

Vtacodty:  a.cohol  in  water      h"dra;hlOTte 

fS :  •  3? 

vapors I3S 

water:  temperature  variation    .    .    .125 

specific:  gases 134 

oils 126 

solutions 129-133 

vapors 134 

water:  temp,  var 125 

Voltaic  cells:  composition,  E.  M.  F.     .    .     252-253 

double-fluid 253 

secondary 253 

single-fluid 252 

standard 251,  253 

storage 253 

Volts,  legal  (international) xxxiv,  251 

Volumes:  critical,  for  gases     .    .    .    .    .    .    .221 


247 
151 
152 
153 
155 
158 
154 
206 
242 
91 
138 
190 
146 
151 
152 
153 
148 
149 
148 
232 


102 
101 
304 
305 
305 
298 
303 
301 

126 


Volumes:  gases,  perfect j62 

glass  vessels,  determinations  of  .     .     .     xx 

Water:   boiling-points  for  various  pressures: 

common  measures  168 
metric  measures   .  169 
densities,  temperature  variation    .     .   95,  96 

ionization  of 273 

solutions  in:   boiling-points      .     .     .     !  219 

densities 93 

diffusion 136 

electrolytic  conduction  272-278 
solutions  of  alcohol,  densities    .     .     .  98-100 

thermal  conductivity  , 200 

vapor  pressure:  low  temperatures      .     .151 
o°  to  100°  C     ....  152 
100°  to  230°  C      ...  153 
vapor,  pressure  of,  in  atmosphere      .     .  155 
(saturated)  weights  of  .     .     .     .154 
viscosity:  absolute,  temp.  var.      .     .     .  125 

specific,  temp,  var 125 

Wave-lengths:  cadmium  red  line 170 

elements,  brighter  lines       .     .     .  170 
Fabry-Buisson  iron  arc  lines  .     .  170 

Fraunhofer  lines 176 

iron  lines,  Fabry-Buisson   .     .     .  170 

Kayser 174 

Kayser  s  iron  arc  lines   ....  174 
Rowland's  solar  lines      .     .     .     .171 
solar  lines  (Rowland)      .     .     .     .171 
Weights  and  measures:   British  to  metric  .     .     9-10 
metric  to  British  .     .     .  7-8 
metric  to  U.  S.     .     .     .       6 

Weights  of  bodies.      .     ^  .S<  f0  ^    .'    .'    !    5! 

Weights  of  sheet  metal 70 

wire:  copper,  iron,  brass: 

common  units     60 
metric  units   .     62 

aluminum,  common  and  metric    .     .    64 
copper  wire,  electrical  constants 

common  units    66 
metric  units  .    68 

Wind  pressures I22 

Wire  gauges:  Birmingham 59 

British  standard 59 

Brown  and  Sharp 66 

Wire,  weights  of:   brass,  copper,  iron    .     .     .  60,  62 

aluminum 64 

copper 66,  68 

Woods:  densities  of 87 

strength  of 72-73 

Young's  modulus  of  elasticity 75  v 

Zonal  harmonics S4 


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